Solve x=C/udy^2

$$x = \frac { C } { u d } y ^ { 2 }$$

Solve for C (complex solution)

$$\left\{\begin{matrix}C=\frac{dux}{y^{2}}\text{, }&u\neq 0\text{ and }d\neq 0\text{ and }y\neq 0\\C\in \mathrm{C}\text{, }&x=0\text{ and }y=0\text{ and }u\neq 0\text{ and }d\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by du.

$$xdu=Cy^{2}$$

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

$$Cy^{2}=xdu$$

The equation is in standard form.

$$y^{2}C=dux$$

Divide both sides by y^{2}.

$$\frac{y^{2}C}{y^{2}}=\frac{dux}{y^{2}}$$

Dividing by y^{2} undoes the multiplication by y^{2}.

$$C=\frac{dux}{y^{2}}$$

Solve for C

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

Steps for Solving Linear Equation

Multiply both sides of the equation by du.

$$xdu=Cy^{2}$$

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

$$Cy^{2}=xdu$$

The equation is in standard form.

$$y^{2}C=dux$$

Divide both sides by y^{2}.

$$\frac{y^{2}C}{y^{2}}=\frac{dux}{y^{2}}$$

Dividing by y^{2} undoes the multiplication by y^{2}.

$$C=\frac{dux}{y^{2}}$$

Solve for d

$$\left\{\begin{matrix}d=\frac{Cy^{2}}{ux}\text{, }&y\neq 0\text{ and }C\neq 0\text{ and }u\neq 0\text{ and }x\neq 0\\d\neq 0\text{, }&\left(y=0\text{ or }C=0\right)\text{ and }x=0\text{ and }u\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable d cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by du.

$$xdu=Cy^{2}$$

Reorder the terms.

$$dux=Cy^{2}$$

The equation is in standard form.

$$uxd=Cy^{2}$$

Divide both sides by xu.

$$\frac{uxd}{ux}=\frac{Cy^{2}}{ux}$$

Dividing by xu undoes the multiplication by xu.

$$d=\frac{Cy^{2}}{ux}$$

Variable d cannot be equal to 0.

$$d=\frac{Cy^{2}}{ux}\text{, }d\neq 0$$