What is the solution for (dx)/(dy)=sqrt(y/5) ?

The solution for (dx)/(dy)=sqrt(y/5) is x= 2/(3sqrt(5))y^{3/2}+c_{1}

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(dx)/(dy)=sqrt(y/5)

\frac{d x}{d y} = \frac{y}{5}

x = \frac{2}{3 5} y^{\frac{3}{2}} + c_{1}

Solution steps

\frac{d x}{d y} = \frac{y}{5}

Substitute

\frac{d x}{d y}

with

x^{'} (y)

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

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

then

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

x = \int \frac{y}{5} d y

\int \frac{y}{5} d y = \frac{2}{3 5} y^{\frac{3}{2}} + c_{1}

x = \frac{2}{3 5} y^{\frac{3}{2}} + c_{1}

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What is the solution for (dx)/(dy)=sqrt(y/5) ?
The solution for (dx)/(dy)=sqrt(y/5) is x= 2/(3sqrt(5))y^{3/2}+c_{1}