Find the answer to this not exact equation The equation (2xy)dx + (y2 - 3x2)dy =

Question

Find the answer to this not exact equation

The equation (2xy)dx + (y2 - 3x2)dy = 0 which is in the form M~dx + N~dy = 0 is not exact. Indeed, we have To solve this problem we will compute an integrating factor as a function of x alone and use it to find the general solution. First we need to check that there is such an integrating factor. For this to be the case we need (M~y - N~x/N~) = ________ to be a function of x alone. Then we find mu(x) as mu(x) = exp( M~y - N~x/N~ dx) = ________ Multiplying the equation by the integrating factor we obtain Mdx + Ndy = 0 with M = ______, ? = _______ We check that this equation is exact by computing My = ____________, Nx = __________ An implicit general solution can be written in the form C = F(x, y) = ___________

Explanation / Answer

This does not look like one that can be solved using an integrating factor.

Make a substitution to form a new and simpler differential equation:
2xy dx + (y

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