Question

The integrating factor of the linear differential equation in \(x\) given by \[ \frac{dy}{dx}=\frac{1}{3x+y+2} \] is

• A. \(e^{-3x}\)
• B. \(e^{-x}\)
• C. \(e^{-3y}\)
• D. \(e^{-y}\)

Hint:

If the given differential equation is not linear in the required variable, first invert it. For \[ \frac{dx}{dy}+Px=Q, \] the integrating factor is \[ \boxed{e^{\int P\,dy}}. \]

Answer 1

The Correct Option is C