Formula:-

(i) if a differential equation is ,

then y(I.F) = ∫Q.(I.F)dx + c, where I.F = e^∫Pdx

(ii) ∫dx = x + c

Here,

This is a linear differential equation, comparing it with

P = 2, Q = e^3x

I.F = e^∫Pdx

= e^∫2dx

= e^2x

multiplying both the sides by I.F

Integrating it with respect to x,

ye^2x = ∫e^5x dx + c