Question

Verify that y=5sin4x is a solution of the differential equation d²y/dx²+16y=0.

Answer 1

Answer :

The given equation is

y = 5 sin4x ...(i)

Now, differentiating both sides with respect to x, we get

dy/dx = 5 d/dx (sin4x)

==> dy/dx = 5 (4 cos4x)

==> dy/dx = 20 cos4x ...(ii)

Again, differentiating both sides with respect to x, we get

d²y/dx² = 20 d/dx (cos4x)

==> d²y/dx² = 20 ( - 4 sin4x )

==> d²y/dx² = - 80 sin4x

==> d²y/dx² = - 16 (5 sin4x)

==> d²y/dx² = - 16y, by (i)

==> d²y/dx² + 16y = 0

Hence, proved.

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