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

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

Solution steps

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

d y - (y - 1)^{2} \cdot d x = 0

- 10 + 4 x + 5 \frac{d x}{d t} = 0

5 x y \frac{d y}{d x} = 2 x, y > 0

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

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