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

The solution for (dy)/(dx)=(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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(dy)/(dx)=(x+xy^2)/(4y)

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

\frac{d y}{d 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

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