Verify that the function satisfies the differential equation.

Ayaana Buck

Ayaana Buck

Answered question

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=2sinx+3
Differential Equation y+y=3

Answer & Explanation

Szeteib

Szeteib

Skilled2021-06-10Added 102 answers

Step 1
Given,
y=2sinx+3
Differentiate the given equation with respect to x we get,
y=2cosx
Now again differentiate with respect to x we get,
y":=2sinx
Step 2
Now,
L.H.S=y"+y
L.H.S=2sinx+2sinx+3
L.H.S=0+3
L.H.S=3
L.H.S=R.H.S

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