What is the solution for x*(dx)/(dy)=4y ?

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

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x*(dx)/(dy)=4y

x \cdot \frac{d x}{d y} = 4 y

y = \frac{c _{1} + x ^{2}}{2}, y = - \frac{c _{1} + x ^{2}}{2}

Solution steps

x \cdot \frac{d}{d y} (x) = 4 y

Solve separable ODE:

y = \frac{c _{1} + x ^{2}}{2}, y = - \frac{c _{1} + x ^{2}}{2}

y = \frac{c _{1} + x ^{2}}{2}, y = - \frac{c _{1} + x ^{2}}{2}

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

\frac{d y}{d x} = y + \frac{y}{x ln ( x )}, y (e) = 1

\frac{d y}{d x} = - x y, y (0) = 1

y^{^{'}} + y = u, y (0) = \frac{- 1}{2}

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

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