We write the equation as
2x2y3dx+x3y2dy−5ydx−7xdy=0Let's select the total differential x^3y^3
31d(x3y3)+x2y3dx−5ydx−7xdy=0.Let's select the total differential -5xy
31d(x3y3)−5d(xy)+x2y3dx−2xdy=0.Consider the equation
x2y3dx−2xdy=0get
xdx=y32dy.As result
2x2+y21=Cwhere C is constant.
Hence. the general solution of the equation is
3x3y3−5xy+2x2+y21=c
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