Question

Find the general solution of the differential equation:

`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`

Answer 1

Given differential equation is `(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`

⇒ `(dy)/(dx) = (3e^(2x)(1 + e^(2x)))/(e^x + 1/e^x)`

⇒ `(dy)/(dx) = (3e^(2x)(1 + e^(2x)))/((e^(2x) + 1)) xx e^x`

⇒ `(dy)/(dx)` = 3e^3x

⇒ dy = 3e^3xdx

Integrating both sides, we get

`intdy = 3inte^(3x)dx`

⇒ y = `3 e^(3x)/3 + C`

y = `e^(3x) + C`