(2xy+3y2)dx-(2xy+X2)dy=0
Let "y(x) = xv(x)", which gives "\\dfrac{dy}{dx}=v+x\\dfrac{dv}{dx}" :
"-(v+x\\dfrac{dv}{dx})( x^2 + 2x^2v) +2x^2v+3x^2v^2 = 0"
Simplify:
"\\dfrac{1+2v}{v(v+1)}dv=\\dfrac{dx}{x}"
"(\\dfrac{1}{v}+\\dfrac{1}{v+1})dv=\\dfrac{dx}{x}"
Integrate
"\\ln(|v|)+\\ln(|v+1|)=\\ln(|x|)+\\ln c_1"
"v(v+1)=c_1x"
"xv(xv+x)=c_1x^3"
"y^2+xy=c_1x^3"
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