Question

if y=e^3x sin 2x, then determine a simplified expression for d^2 y/ dx^2 - 4 dy/dx + 9y.

Answer 1

y = e^3x sin2x
y' = e^3x (3sin2x + 2cos2x)
y" = e^3x (5sin2x + 12cos2x)
so, y" - 4y' + 9y = 2e^3x (17sin2x + 50cos2x)