# Verify that the function satisfies the differential equation.

Equations

Verify that the function satisfies the differential equation. (A differential equation in x and y is an equation that involves x, y, and derivatives of y.) Function $$y = 2 \sin x + 3$$
Differential Equation $$y'' + y = 3$$

2021-06-10

Step 1
Given,
$$y=2 \sin x+3$$
Differentiate the given equation with respect to x we get,
$$y'=2 \cos x$$
Now again differentiate with respect to x we get,
$$y":=−2\sin x$$
Step 2
Now,
$$L.H.S=y"+y$$
$$L.H.S=−2\sin x+2\sin x+3$$
$$L.H.S=0+3$$
$$L.H.S=3$$
$$L.H.S=R.H.S$$