What is the solution for (dy)/(dx)=(x+xy^2)/(4y),y(1)=0 ?

The solution for (dy)/(dx)=(x+xy^2)/(4y),y(1)=0 is y=sqrt(e^{(x^2-1)/4)-1},y=-sqrt(e^{(x^2-1)/4)-1}

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(dy)/(dx)=(x+xy^2)/(4y),y(1)=0

\frac{d y}{d x} = \frac{x + x y ^{2}}{4 y}, y (1) = 0

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} + 6 x^{2} y = 7 x^{2}, y (0) = 2

\frac{2 d y}{d t} + y = 0

y^{^{'}} = y^{2} e^{- t}, y (0) = \frac{1}{2}

\frac{d y}{d x} = \frac{e ^{8 y + x}}{x}, x > 0

y^{^{'}} = 8 x sec (y)

What is the solution for (dy)/(dx)=(x+xy^2)/(4y),y(1)=0 ?
The solution for (dy)/(dx)=(x+xy^2)/(4y),y(1)=0 is y=sqrt(e^{(x^2-1)/4)-1},y=-sqrt(e^{(x^2-1)/4)-1}