S Therefore, the given function is a solution of the given differential equation Example 3 Verify that the function y = a cos x + b sin x, where, a, b ∈ R is a solution
of the differential equation 
2
2
0
d y
y
dx
+
=
Solution The given function is
y = a cos x + b sin x (1)
Differentiating both sides of equation (1) with respect to x, successively, we get
dy
dx  = – a sinx + b cosx
2
d y2
dx
 = – a cos x – b sinx
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DIFFERENTIAL EQUATIONS
385
Substituting the values of 
2
d y2
dx
 and y in the given differential equation, we get
L