Consider the ODE y' = y2/x subject to the boundary condition y(1)=1. Find an implicit solution of the form H(x,y) = constant, then find an explicit solution of the form y=y(x). What is the largest x-interval on which the solution is defined?
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Here is the solution.
The first part is finding an integration factor for a non-exact equation.
The full process is described in:
Can be rewritten as:
This is a non exact equation ...
A step by step process, the solution illustrates two methods to solve the equation. The solution is five pages long of full derivations.