How to solve differential equation with absolute value?












2














I'm a newbie here, I want to solve this equation for my assignment:



mg - c x'[t] Abs[x'[t]] = m x''[t]


I'm using



DSolve[{mg - c x'[t] Abs[x'[t]] == m x''[t],x'[0]==0,x[0]==32000},x[t],t]


but Mathematica seems very slow to load.



Questions: is there any other way to solve the equation?



Edit: i've tried to change, but still doesn't work
enter image description here






differential-equations







share|improve this question









New contributor




J. Manopo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • 1




    You should check the boundary conditions: x[0]== 32000 , x'[0] makes no sense!
    – Ulrich Neumann
    1 hour ago










  • The defintion of the ode is wrong: mg - c x'[t] Abs[x'[t]] == m x''[t]
    – Ulrich Neumann
    1 hour ago










  • i forgot to write x'[0]==0
    – J. Manopo
    1 hour ago
















2














I'm a newbie here, I want to solve this equation for my assignment:



mg - c x'[t] Abs[x'[t]] = m x''[t]


I'm using



DSolve[{mg - c x'[t] Abs[x'[t]] == m x''[t],x'[0]==0,x[0]==32000},x[t],t]


but Mathematica seems very slow to load.



Questions: is there any other way to solve the equation?



Edit: i've tried to change, but still doesn't work
enter image description here






differential-equations







share|improve this question









New contributor




J. Manopo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 1




    You should check the boundary conditions: x[0]== 32000 , x'[0] makes no sense!
    – Ulrich Neumann
    1 hour ago










  • The defintion of the ode is wrong: mg - c x'[t] Abs[x'[t]] == m x''[t]
    – Ulrich Neumann
    1 hour ago










  • i forgot to write x'[0]==0
    – J. Manopo
    1 hour ago














2












2








2







I'm a newbie here, I want to solve this equation for my assignment:



mg - c x'[t] Abs[x'[t]] = m x''[t]


I'm using



DSolve[{mg - c x'[t] Abs[x'[t]] == m x''[t],x'[0]==0,x[0]==32000},x[t],t]


but Mathematica seems very slow to load.



Questions: is there any other way to solve the equation?



Edit: i've tried to change, but still doesn't work
enter image description here






differential-equations







share|improve this question









New contributor




J. Manopo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











I'm a newbie here, I want to solve this equation for my assignment:



mg - c x'[t] Abs[x'[t]] = m x''[t]


I'm using



DSolve[{mg - c x'[t] Abs[x'[t]] == m x''[t],x'[0]==0,x[0]==32000},x[t],t]


but Mathematica seems very slow to load.



Questions: is there any other way to solve the equation?



Edit: i've tried to change, but still doesn't work
enter image description here






differential-equations




differential-equations






share|improve this question









New contributor




J. Manopo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|improve this question









New contributor




J. Manopo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|improve this question




share|improve this question








edited 1 hour ago





















New contributor




J. Manopo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 2 hours ago









J. Manopo

183




183




New contributor




J. Manopo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





J. Manopo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






J. Manopo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 1




    You should check the boundary conditions: x[0]== 32000 , x'[0] makes no sense!
    – Ulrich Neumann
    1 hour ago










  • The defintion of the ode is wrong: mg - c x'[t] Abs[x'[t]] == m x''[t]
    – Ulrich Neumann
    1 hour ago










  • i forgot to write x'[0]==0
    – J. Manopo
    1 hour ago














  • 1




    You should check the boundary conditions: x[0]== 32000 , x'[0] makes no sense!
    – Ulrich Neumann
    1 hour ago










  • The defintion of the ode is wrong: mg - c x'[t] Abs[x'[t]] == m x''[t]
    – Ulrich Neumann
    1 hour ago










  • i forgot to write x'[0]==0
    – J. Manopo
    1 hour ago








1




1




You should check the boundary conditions: x[0]== 32000 , x'[0] makes no sense!
– Ulrich Neumann
1 hour ago




You should check the boundary conditions: x[0]== 32000 , x'[0] makes no sense!
– Ulrich Neumann
1 hour ago












The defintion of the ode is wrong: mg - c x'[t] Abs[x'[t]] == m x''[t]
– Ulrich Neumann
1 hour ago




The defintion of the ode is wrong: mg - c x'[t] Abs[x'[t]] == m x''[t]
– Ulrich Neumann
1 hour ago












i forgot to write x'[0]==0
– J. Manopo
1 hour ago




i forgot to write x'[0]==0
– J. Manopo
1 hour ago










1 Answer
1






active

oldest

votes


















3














If you substitute Abs[x'[t]]->Sqrt[x'[t]^2] mathematica can evaluate the ode



DSolve[{mg - c x'[t] Sqrt[x'[t]^2] == m x''[t] }, x[t], t]


Unfortunately the solution cannot be adapted to the inital conditions x'[0]==0, x[0]== 32000



workaraound



The ode only depends on x'[t],x''[t], the substitution x'[t]->v[t] and division by m gives 



ode=9.81 - cdm  v[t] Sqrt[v[t]^2] ==   v'[t] (*g=9.81*)


ode only depends on parameters cdm=c/m , v0 and can be solved numerically



X = ParametricNDSolveValue[{ode,v[0] == v0 }, v, {t, 0, 10}, {v0, cdm}]

Plot[X[.0 , 1  ][t], {t, 0, 1}, PlotRange -> {0, Automatic}]


enter image description here






share|improve this answer



















  • 1




    i've tried it, but still doesn't work.
    – J. Manopo
    1 hour ago










  • The problem seems to be the initial condition x'[0]==0. You give numerical values for the initial conditions, perhaps you can provide the parameter values m, g, ctoo?
    – Ulrich Neumann
    50 mins ago











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1 Answer
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1 Answer
1






active

oldest

votes









active

oldest

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active

oldest

votes









3














If you substitute Abs[x'[t]]->Sqrt[x'[t]^2] mathematica can evaluate the ode



DSolve[{mg - c x'[t] Sqrt[x'[t]^2] == m x''[t] }, x[t], t]


Unfortunately the solution cannot be adapted to the inital conditions x'[0]==0, x[0]== 32000



workaraound



The ode only depends on x'[t],x''[t], the substitution x'[t]->v[t] and division by m gives 



ode=9.81 - cdm  v[t] Sqrt[v[t]^2] ==   v'[t] (*g=9.81*)


ode only depends on parameters cdm=c/m , v0 and can be solved numerically



X = ParametricNDSolveValue[{ode,v[0] == v0 }, v, {t, 0, 10}, {v0, cdm}]

Plot[X[.0 , 1  ][t], {t, 0, 1}, PlotRange -> {0, Automatic}]


enter image description here






share|improve this answer



















  • 1




    i've tried it, but still doesn't work.
    – J. Manopo
    1 hour ago










  • The problem seems to be the initial condition x'[0]==0. You give numerical values for the initial conditions, perhaps you can provide the parameter values m, g, ctoo?
    – Ulrich Neumann
    50 mins ago
















3














If you substitute Abs[x'[t]]->Sqrt[x'[t]^2] mathematica can evaluate the ode



DSolve[{mg - c x'[t] Sqrt[x'[t]^2] == m x''[t] }, x[t], t]


Unfortunately the solution cannot be adapted to the inital conditions x'[0]==0, x[0]== 32000



workaraound



The ode only depends on x'[t],x''[t], the substitution x'[t]->v[t] and division by m gives 



ode=9.81 - cdm  v[t] Sqrt[v[t]^2] ==   v'[t] (*g=9.81*)


ode only depends on parameters cdm=c/m , v0 and can be solved numerically



X = ParametricNDSolveValue[{ode,v[0] == v0 }, v, {t, 0, 10}, {v0, cdm}]

Plot[X[.0 , 1  ][t], {t, 0, 1}, PlotRange -> {0, Automatic}]


enter image description here






share|improve this answer



















  • 1




    i've tried it, but still doesn't work.
    – J. Manopo
    1 hour ago










  • The problem seems to be the initial condition x'[0]==0. You give numerical values for the initial conditions, perhaps you can provide the parameter values m, g, ctoo?
    – Ulrich Neumann
    50 mins ago














3












3








3






If you substitute Abs[x'[t]]->Sqrt[x'[t]^2] mathematica can evaluate the ode



DSolve[{mg - c x'[t] Sqrt[x'[t]^2] == m x''[t] }, x[t], t]


Unfortunately the solution cannot be adapted to the inital conditions x'[0]==0, x[0]== 32000



workaraound



The ode only depends on x'[t],x''[t], the substitution x'[t]->v[t] and division by m gives 



ode=9.81 - cdm  v[t] Sqrt[v[t]^2] ==   v'[t] (*g=9.81*)


ode only depends on parameters cdm=c/m , v0 and can be solved numerically



X = ParametricNDSolveValue[{ode,v[0] == v0 }, v, {t, 0, 10}, {v0, cdm}]

Plot[X[.0 , 1  ][t], {t, 0, 1}, PlotRange -> {0, Automatic}]


enter image description here






share|improve this answer














If you substitute Abs[x'[t]]->Sqrt[x'[t]^2] mathematica can evaluate the ode



DSolve[{mg - c x'[t] Sqrt[x'[t]^2] == m x''[t] }, x[t], t]


Unfortunately the solution cannot be adapted to the inital conditions x'[0]==0, x[0]== 32000



workaraound



The ode only depends on x'[t],x''[t], the substitution x'[t]->v[t] and division by m gives 



ode=9.81 - cdm  v[t] Sqrt[v[t]^2] ==   v'[t] (*g=9.81*)


ode only depends on parameters cdm=c/m , v0 and can be solved numerically



X = ParametricNDSolveValue[{ode,v[0] == v0 }, v, {t, 0, 10}, {v0, cdm}]

Plot[X[.0 , 1  ][t], {t, 0, 1}, PlotRange -> {0, Automatic}]


enter image description here







share|improve this answer














share|improve this answer



share|improve this answer








edited 14 mins ago

























answered 1 hour ago









Ulrich Neumann

7,122515




7,122515








  • 1




    i've tried it, but still doesn't work.
    – J. Manopo
    1 hour ago










  • The problem seems to be the initial condition x'[0]==0. You give numerical values for the initial conditions, perhaps you can provide the parameter values m, g, ctoo?
    – Ulrich Neumann
    50 mins ago














  • 1




    i've tried it, but still doesn't work.
    – J. Manopo
    1 hour ago










  • The problem seems to be the initial condition x'[0]==0. You give numerical values for the initial conditions, perhaps you can provide the parameter values m, g, ctoo?
    – Ulrich Neumann
    50 mins ago








1




1




i've tried it, but still doesn't work.
– J. Manopo
1 hour ago




i've tried it, but still doesn't work.
– J. Manopo
1 hour ago












The problem seems to be the initial condition x'[0]==0. You give numerical values for the initial conditions, perhaps you can provide the parameter values m, g, ctoo?
– Ulrich Neumann
50 mins ago




The problem seems to be the initial condition x'[0]==0. You give numerical values for the initial conditions, perhaps you can provide the parameter values m, g, ctoo?
– Ulrich Neumann
50 mins ago










J. Manopo is a new contributor. Be nice, and check out our Code of Conduct.










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