Question

If y = ex(sin x + cosx), prove that y2 – 2y1 + 2y = 0

Answer 1

Given y = ex(sinx + cosx),

⇒ dy/dx = ex(sin x + cos x) + ex(cosx – sinx)

⇒ dy/dx = 2excos x

⇒ d2y/dx2 = 2ex (cosx – sinx)

Now, d2y/dx2 – 2dy/dx + 2y

= 2ex(cosx – sinx) – 4excos x + 2ex(sinx + cosx)

= 2ex(cosx – sinx – 2cosx + sinx + cos x)

= 2ex (0)

= 0.