My equation is
[{x[t]*x'[t])'-(F/m)+(b/m)*x(t)*x'(t)==0},x(0)=0,x'(0)=0]
It is a form of Newtons momentum equation, but I am having a lot of trouble solving this in Mathematica. Is DSolve the correct method to go about this?
Are you sure about the initial conditions?
DSolve is the right method. Observing that only the product x[t]x'[t]
occurs the substitution x[t]x'[t]->u[t]
gives a first order ode which can be solved for u[t]
U = DSolveValue[ {D[u[t] , t] - (F/m) + (b/m)*u[t] == 0 }, u, t]
(*Function[{t}, F/b + E^(-((b t)/m)) C[1]]*)
Resubstituting u[t] gives the solution x[t]
X = DSolveValue[{x[t] x'[t] == U[t] }, x, t]
(*Function[{t}, -((Sqrt[2] Sqrt[F t - E^(-((b t)/m)) m C[1] + b C[2]])/Sqrt[b])]*)
That is the general solution of your problem! The parameters C[1],C[2]
must be choosen to fullfill the initial conditions
{X[0], X'[0]}
(*{-((Sqrt[2] Sqrt[-m C[1] + b C[2]])/Sqrt[b]), -((F + b C[1])/(Sqrt[2] Sqrt[b] Sqrt[-m C[1] + b C[2]]))}*)
Unfortunately it is not possible to adapt your initial conditions x[0]==0,x'[0]==0
Please read these introductions before continuing. What appears to be the function you want is DSolve[{\!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\((x[t]*\(x'\)[t])\)\) - (F/
m) + (b/m)*x[t]*x'[t] == 0, x[0] == 0, x'[0] == 0}, x[t], t]
, which has no solutions for your initial conditions.
The Four Kinds of Bracketing in the Wolfram Language
$\endgroup$DSolve
is the first function to try in this case. $\endgroup$