Solve dy=2C/dydt

$$d y = \frac { 2 C } { d } y d t$$

Solve for C (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by d.

$$dyd=2Cydt$$

Multiply d and d to get d^{2}.

$$d^{2}y=2Cydt$$

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

$$2Cydt=d^{2}y$$

The equation is in standard form.

$$2dtyC=yd^{2}$$

Divide both sides by 2ydt.

$$\frac{2dtyC}{2dty}=\frac{yd^{2}}{2dty}$$

Dividing by 2ydt undoes the multiplication by 2ydt.

$$C=\frac{yd^{2}}{2dty}$$

Divide d^{2}y by 2ydt.

$$C=\frac{d}{2t}$$

Solve for C

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

Steps for Solving Linear Equation

Multiply both sides of the equation by d.

$$dyd=2Cydt$$

Multiply d and d to get d^{2}.

$$d^{2}y=2Cydt$$

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

$$2Cydt=d^{2}y$$

The equation is in standard form.

$$2dtyC=yd^{2}$$

Divide both sides by 2ydt.

$$\frac{2dtyC}{2dty}=\frac{yd^{2}}{2dty}$$

Dividing by 2ydt undoes the multiplication by 2ydt.

$$C=\frac{yd^{2}}{2dty}$$

Divide d^{2}y by 2ydt.

$$C=\frac{d}{2t}$$

Solve for d

$$\left\{\begin{matrix}d=2Ct\text{, }&t\neq 0\text{ and }C\neq 0\\d\neq 0\text{, }&y=0\end{matrix}\right.$$