What is the solution for (dx)/(dy)=sqrt(y/2) ?

The solution for (dx)/(dy)=sqrt(y/2) is x=(sqrt(2))/3 y^{3/2}+c_{1}

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(dx)/(dy)=sqrt(y/2)

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

x = \frac{2}{3} y^{\frac{3}{2}} + c_{1}

Solution steps

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

Substitute

\frac{d x}{d y}

with

x^{'} (y)

x^{^{'}} (y) = \frac{y}{2}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

x = \int \frac{y}{2} d y

\int \frac{y}{2} d y = \frac{2}{3} y^{\frac{3}{2}} + c_{1}

x = \frac{2}{3} y^{\frac{3}{2}} + c_{1}

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What is the solution for (dx)/(dy)=sqrt(y/2) ?
The solution for (dx)/(dy)=sqrt(y/2) is x=(sqrt(2))/3 y^{3/2}+c_{1}