Solve y=sqrt{x}dx

$$y = \sqrt { x } d x$$

Solve for d

$$\left\{\begin{matrix}d=\frac{y}{x^{\frac{3}{2}}}\text{, }&x>0\\d\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{x}dx=y$$

The equation is in standard form.

$$\sqrt{x}xd=y$$

Divide both sides by \sqrt{x}x.

$$\frac{\sqrt{x}xd}{\sqrt{x}x}=\frac{y}{\sqrt{x}x}$$

Dividing by \sqrt{x}x undoes the multiplication by \sqrt{x}x.

$$d=\frac{y}{\sqrt{x}x}$$

Divide y by \sqrt{x}x.

$$d=\frac{y}{x^{\frac{3}{2}}}$$

Solve for x

$$\left\{\begin{matrix}x=\left(\frac{y}{d}\right)^{\frac{2}{3}}\text{, }&\left(y\geq 0\text{ and }d>0\right)\text{ or }\left(y\leq 0\text{ and }d<0\right)\\x\geq 0\text{, }&y=0\text{ and }d=0\end{matrix}\right.$$