Assuming that I have a ODE system with undetermined parameter $$x''(t) == y(t) x(t)$$ $$y'(t) == 2 - a x(t)$$
and I have some fixed solution condition $$x(0)=0$$ $$x(10)=8$$ $$y(10)=3.5$$
Is there a way to determine the parameter a
,
I tried to solve this ODEs with both NDSolve
and DSolve
, but it seems not to work.
NDSolve[{x''[t] == y[t] x[t], y'[t] == 2 - a x[t], x[0] == 0,
x[10] == 8, y[10] == 3.5}, {x, y}, t]
the output is
NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.`.
can somebody help me? Thank you very much.
a
you need one more condition. Three conditions are required to solve the differential equations for a particular parameter, since you've got (effectively) a third-order ordinary differential equation. $\endgroup$a
is a real number $\endgroup$