Question

Solve:

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

Answer 1

`dy/dx + 2x = e^(3x)`    ...[Given]

⇒ `dy/dx = e^(3x) − 2x`

On integrating both sides

⇒ ∫dy = ∫(e^3x − 2x)dx

⇒ y = `(e^(3x))/(3) − (2x^2)/2 + c`      ...[∵ ∫e^x = e^x + c]

y = `(e^(3x))/3 − x^2 + c`