Solve y^prime=jy-4/z-4=

$$y ^ { \prime } = \frac { j y - 4 } { z - 4 } =$$

Solve for j

$$j=\frac{4}{y}$$

$$y\neq 0\text{ and }z\neq 4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by z-4.

$$\left(z-4\right)\frac{\mathrm{d}}{\mathrm{d}x}(y)=jy-4$$

Use the distributive property to multiply z-4 by \frac{\mathrm{d}}{\mathrm{d}x}(y).

$$z\frac{\mathrm{d}}{\mathrm{d}x}(y)-4\frac{\mathrm{d}}{\mathrm{d}x}(y)=jy-4$$

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

$$jy-4=z\frac{\mathrm{d}}{\mathrm{d}x}(y)-4\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Add 4 to both sides.

$$jy=z\frac{\mathrm{d}}{\mathrm{d}x}(y)-4\frac{\mathrm{d}}{\mathrm{d}x}(y)+4$$

The equation is in standard form.

$$yj=4$$

Divide both sides by y.

$$\frac{yj}{y}=\frac{4}{y}$$

Dividing by y undoes the multiplication by y.

$$j=\frac{4}{y}$$

Solve for x

$$x\in \mathrm{R}$$

$$y=\frac{4}{j}\text{ and }j\neq 0\text{ and }z\neq 4$$