What is the solution for y^'=((y^2+xy-x^2))/(x^2) ?

The solution for y^'=((y^2+xy-x^2))/(x^2) is y=(e^{2c_{1}}x^3)/(1-e^{2c_{1)}x^2}+x/(1-e^{2c_{1)}x^2}

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y^'=((y^2+xy-x^2))/(x^2)

y^{^{'}} = \frac{( y ^{2} + x y - x ^{2} )}{x ^{2}}

y = \frac{e ^{2 c_{1}} x ^{3}}{1 - e ^{2 c_{1}} x ^{2}} + \frac{x}{1 - e ^{2 c_{1}} x ^{2}}

Solution steps

y^{'} (x) = \frac{( y ^{2} + x y - x ^{2} )}{x ^{2}}

Solve using substitution:

y = \frac{e ^{2 c_{1}} x ^{3}}{1 - e ^{2 c_{1}} x ^{2}} + \frac{x}{1 - e ^{2 c_{1}} x ^{2}}

y = \frac{e ^{2 c_{1}} x ^{3}}{1 - e ^{2 c_{1}} x ^{2}} + \frac{x}{1 - e ^{2 c_{1}} x ^{2}}

What is the solution for y^'=((y^2+xy-x^2))/(x^2) ?
The solution for y^'=((y^2+xy-x^2))/(x^2) is y=(e^{2c_{1}}x^3)/(1-e^{2c_{1)}x^2}+x/(1-e^{2c_{1)}x^2}