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

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

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

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

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

Solution steps

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

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