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Answer to Question #20864 in Differential Equations for behzad

Question #20864
y^2dx=(x^3-xy)dy
Expert's answer
y^2dx=(x^3-xy)dx
xy=u
u'=x'y+x
y^2x'(y)=(x^3-xy)dx
x'(y)=u'/y+x
yu'(y)-xy=x^3-xy
yu'(y)=u^3(y)/y^3
y^4u'(y)=u^3(y)
y^-4dy=u^-3du
y^-3/3=u^-2/2+C
u=Sqrt(1.5y^3+C)
x=u/y
x(y)=Sqrt(1.5y^3+C)/y

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