my question is on initial value problem for ODE's..
iv been asked to solve the following IVP:
dx/dt = (x^2)*(cos 2t) for x(pi/4)=0
Basically iv rearranged this and integrated to get
-1/x = 1/2*sin2t + c
But the problem came when i had to put in the values for x and t, when i plug x into the equation, i get -1/0, for which i cant do ....urm i dont know what to do next ...any help?? thankz
I'm not certain why the standard solution method doesn't provide the x(t) = 0 solution. My best guess would be that the DE is non-linear. In any event, your problem with finding a C that fits the initial conditions is that the solution method you used has no solution that passes though the point given as the initial condition. Hence we have to look for other solutions using any method we can think of, a pretty hairy task in general. Fortunately the x(t) = 0 solution is obvious once it is looked for.