What is the solution for y^'= x/(5y) ?

The solution for y^'= x/(5y) is y=sqrt((x^2)/5+c_{1)},y=-sqrt((x^2)/5+c_{1)}

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y^'= x/(5y)

y^{^{'}} = \frac{x}{5 y}

y = \frac{x ^{2}}{5} + c_{1}, y = - \frac{x ^{2}}{5} + c_{1}

Solution steps

y^{'} (x) = \frac{x}{5 y}

Solve separable ODE:

y = \frac{x ^{2}}{5} + c_{1}, y = - \frac{x ^{2}}{5} + c_{1}

y = \frac{x ^{2}}{5} + c_{1}, y = - \frac{x ^{2}}{5} + c_{1}

y^{^{'}} = e^{- y} - x e^{- y} cos (x^{2})

4 y^{^{'}} - 4 e^{2 x} y = 0, y (0) = 3

4 (1 + y^{2}) d x - x y d y = 0

\frac{d y}{d t} + y t sin (t) = 0

\frac{d y}{d x} = \frac{3 x ^{2} + 4 x + 2}{2 y - 2}

What is the solution for y^'= x/(5y) ?
The solution for y^'= x/(5y) is y=sqrt((x^2)/5+c_{1)},y=-sqrt((x^2)/5+c_{1)}