What is the solution for xy^'-2y+y^2=0 ?

The solution for xy^'-2y+y^2=0 is y=-(2e^{2c_{1}}x^2)/(1-e^{2c_{1)}x^2}

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xy^'-2y+y^2=0

x y^{^{'}} - 2 y + y^{2} = 0

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

Solution steps

x y^{'} (x) - 2 y + y^{2} = 0

Solve separable ODE:

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

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

y^{^{''}} + 2 k y^{^{'}} + k^{4} y = 0

(9, 12), (- 2, - 17)

\int \frac{x ^{2}}{( x + 1 ) ( x + 2 ) ^{2}} d x

\int x^{2} e^{x y} d y

\int e^{\frac{- x}{3}} d x

What is the solution for xy^'-2y+y^2=0 ?
The solution for xy^'-2y+y^2=0 is y=-(2e^{2c_{1}}x^2)/(1-e^{2c_{1)}x^2}