Question

Verify that the function satisfies the differential equation.

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asked 2021-06-09

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 \(y'' + y = 3\)

Answers (1)

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,
\(L.H.S=y"+y\)
\(L.H.S=−2\sin x+2\sin x+3\)
\(L.H.S=0+3\)
\(L.H.S=3\)
\(L.H.S=R.H.S\)

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