Q. 2 B3.6( 8 Votes )
For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.
y = ex (a cos x + b sin x) :
It is given that y = ex(acosx + bsinx) = aexcosx + bexsinx
Now, differentiating both sides w.r.t. x, we get,
Now, again differentiating both sides w.r.t. x, we get,
Now, Substituting the values of ’ and in the given differential equations, we get,
=2ex(bcosx – asinx) -2ex[(a + b)cosx + (b –a ) sinx] + 2ex(acosx + bsinx)
=ex[(2bcosx – 2asinx) - (2acosx + 2bcosx) - (2bsinx – 2asinx) + (2acosx + 2bsinx)]
= ex[(2b – 2a – 2b + 2a)cosx] + ex[(-2a – 2b + 2a + 2bsinx]
= 0 = RHS.
Therefore, the given function is the solution of the corresponding differential equation.
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