Can anyone differentiate this

y=e^xsinx show that d^2y/dx^2+2(dy/dx)+2y=0
thanks!! please do it in steps :)

If y = e^x sin x, then the DE should be y'' - 2y' + 2y = 0.

Use the product rule.
y' = e^x sin x + e^x cos x = e^x (sin x + cos x)
and y'' = e^x (sin x + cos x) + e^x (cos x - sin x) = 2 e^x cos x.

Therefore, y'' - 2y' + 2y
= 2 e^x cos x - 2(e^x (sin x + cos x)) + 2(e^x sin x)
= 0.

I hope this helps!