Solve y+x^prime=3y

$$y + x ^ { \prime } = 3 y$$

Solve for y

$$y = \frac{1}{2} = 0.5$$

Steps for Solving Linear Equation

Subtract 3y from both sides.

$$y+\frac{\mathrm{d}}{\mathrm{d}x}(x)-3y=0$$

Combine y and -3y to get -2y.

$$-2y+\frac{\mathrm{d}}{\mathrm{d}x}(x)=0$$

Subtract \frac{\mathrm{d}}{\mathrm{d}x}(x) from both sides. Anything subtracted from zero gives its negation.

$$-2y=-\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

The equation is in standard form.

$$-2y=-1$$

Divide both sides by -2.

$$\frac{-2y}{-2}=-\frac{1}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$y=-\frac{1}{-2}$$

Divide -1 by -2.

$$y=\frac{1}{2}$$

Solve for x

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

$$y = \frac{1}{2} = 0.5$$