At the moment this is unsolvable exactly.
Are you sure you haven't got a "square" in the wrong spot. If it was
this would be separable...
I've been given the following ODE to be solved:
But I don't really know how to start. A direct integration is (obviously enough) not possible and it's not in the form to be solved by an integrating factor (or so I understand).
Then it could be solved by separation of variables (though I can't see what the separation itself would be), or by using the exact equation technique (though I'm not even sure how to check if it's in the appropriate form).
How do I get started?
I just double, no, triple-checked it here, and the square is indeed at the "y", as I posted it. What might have happened is that the professor mistyped it when writing the exam (I'm doing a post-mortem), but that would be at least unexpected since I don't remember anybody complaining about it during the exam nor did he make any corrections.
So, the equation as I originally posted is not solvable at all? What does "unsolvable exactly" mean? Because, according to Wolfram Alpha (solve - Wolfram|Alpha[(y+x^2)dy/dx+%2B+2y^2+x+%2B+3x^3+%3D%3D+0]), it does give me a solution.
PS: I forgot to mention, the original problem says to solve the IVP given by the equation I posted and the condition