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

The solution for 2y(dy)/(dx)-xy^2=x is y=sqrt(e^{(x^2)/2+c_{1)}-1},y=-sqrt(e^{(x^2)/2+c_{1)}-1}

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2y(dy)/(dx)-xy^2=x

2 y \frac{d y}{d x} - x y^{2} = x

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

Solution steps

2 y \frac{d y}{d x} - x y^{2} = x

Solve separable ODE:

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

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

\frac{d}{d x} (arcsin (x) - 2 x)

\frac{( 5 x ^{2} + 9 ) ^{5}}{( x - 3 ) ^{4}}

\int x y^{3} d x

\int x^{3} tan^{3} (x^{4}) d x

f (x) = 3 x

What is the solution for 2y(dy)/(dx)-xy^2=x ?
The solution for 2y(dy)/(dx)-xy^2=x is y=sqrt(e^{(x^2)/2+c_{1)}-1},y=-sqrt(e^{(x^2)/2+c_{1)}-1}