If y = ex(sin x + cos x) then show that d2y/dx2 - 2(dy/dx) + 2y = 0 – InterviewSolution

1.

If y = ex(sin x + cos x) then show that d2y/dx2 - 2(dy/dx) + 2y = 0

Answer»

y = e^x(sin x + cos x)

Differentiating w.r.t x, we get

dy/dx = e^x(d(sin x + cos x)/dx)

= e^x(cos x - sin x)

Again differentiating w.r.t x, we get

d²y/dx² = -e^x(sin x - cos x)

d²y/dx² = -2(dy/dx) + 2y = 0

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