Question

Find the general solution of the following equation.y '(x) + 2y = -4

Equations

Find the general solution of the following equation.
$$y '(x) + 2y = -4$$

2021-05-19

Step 1
Given
$$y '(x) + 2y = -4$$
Calculation:
Step 2
$$y'+2y=-4$$
$$\frac{dy}{dx}+2y=-4$$
$$I.F.=e^{\int 2dx}$$
$$I.F.=e^{2x}$$
$$y\times I.F.=\int -4\times I.F.$$
$$y\times e^{2x}=\int -4\times e^{2x}dx$$
$$ye^{2x}=-4\int e^{2x}dx$$
$$ye^{2x}=-4\times \frac{e^{2x}}{2}+C$$
$$ye^{2x}=-2e^{2x}+C$$
$$y=-2+Ce^{-2x}$$