Solve C(A)-C(B)=dv/dx

$$C ( A ) - C ( B ) = \frac { d v } { d x }$$

Solve for A

$$\left\{\begin{matrix}A=B\text{, }&C\neq 0\\A\in \mathrm{R}\text{, }&C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add CB to both sides.

$$CA=\frac{\mathrm{d}}{\mathrm{d}x}(v)+CB$$

The equation is in standard form.

$$CA=BC$$

Divide both sides by C.

$$\frac{CA}{C}=\frac{BC}{C}$$

Dividing by C undoes the multiplication by C.

$$A=\frac{BC}{C}$$

Divide CB by C.

$$A=B$$

Solve for B

$$\left\{\begin{matrix}B=A\text{, }&C\neq 0\\B\in \mathrm{R}\text{, }&C=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract CA from both sides.

$$-CB=\frac{\mathrm{d}}{\mathrm{d}x}(v)-CA$$

The equation is in standard form.

$$\left(-C\right)B=-AC$$

Divide both sides by -C.

$$\frac{\left(-C\right)B}{-C}=-\frac{AC}{-C}$$

Dividing by -C undoes the multiplication by -C.

$$B=-\frac{AC}{-C}$$

Divide -CA by -C.

$$B=A$$