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(2xy−9x2)dx+(2y+x2+1)dy=0My=2x=Nx=2x∫M dx+g(y)H(x,y)=∫2xy−9x2dx+g(y)=∫2y+x2+1 dy=x2y−3x3+g(y)=y2+x2y+y
Since x2y appears on both sides, cancel it on the yside, which gives g(y)=y2+y. Add this to the leftside and the general solution is:
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