What is the solution for y^'=(x+xy^2)/(4y) ?

The solution for y^'=(x+xy^2)/(4y) is y=sqrt(e^{(x^2)/4+c_{1)}-1},y=-sqrt(e^{(x^2)/4+c_{1)}-1}

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y^'=(x+xy^2)/(4y)

y^{^{'}} = \frac{x + x y ^{2}}{4 y}

y = e^{\frac{x ^{2}}{4} + c_{1}} - 1, y = - e^{\frac{x ^{2}}{4} + c_{1}} - 1

Solution steps

y^{'} (x) = \frac{x + x y ^{2}}{4 y}

Solve separable ODE:

y = e^{\frac{x ^{2}}{4} + c_{1}} - 1, y = - e^{\frac{x ^{2}}{4} + c_{1}} - 1

y = e^{\frac{x ^{2}}{4} + c_{1}} - 1, y = - e^{\frac{x ^{2}}{4} + c_{1}} - 1

\frac{d x}{d t} = 30 - \frac{x}{100}

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

\frac{d y}{d x} = \frac{20 x ^{4}}{y}

\frac{d y}{d x} = 0.2 x y

\frac{d y}{d x} = \frac{2 ( 1 + x )}{x y}

What is the solution for y^'=(x+xy^2)/(4y) ?
The solution for y^'=(x+xy^2)/(4y) is y=sqrt(e^{(x^2)/4+c_{1)}-1},y=-sqrt(e^{(x^2)/4+c_{1)}-1}