Let us take y = e^x sin 5x

Now,

= e^xsin5x+e^xcos5x.5

= e^x (sin5x + 5cos5x)

= e^x (sin5x + 5cos5x) + e^x (5cos5x – 25sin5x)

= e^x (10cos5x – 24sin5x)

= 2e^x (5cos5x – 12sin5x)