I'm Leonardo and I'm a maths student from Trento,Italy.
I'm trying to solve analitically a Cauchy Problem which involves an ordonary differential equation of the form:
$\frac{dX(t)}{dt}+ a(t)X(t)^2=b(t)$ , with the following initial condition $X(0)=0$.
I know how to solve the corresponding homogeneous problem, with the method of separation of variables, but I don't know how to relate the solution of the homogeneous case, with the general problem. Is there any operative method?
I also know that the function $a(t)\rightarrow 0$ as $t\rightarrow 0$ and that the function $b(t)$ is linear.
Could anybody help me with this or give me some hints, please? That would be really appreciated :). Thanks to all for your time in advance.
Regards.