Question

The general solution of a differential equation of the type \(\frac{dx}{dy}+p_{1}x=Q1\) is

• A. \(ye^{\int{p_{1}dy}}=\int{(Q_{1}e^{\int{p_{1}dy}})}dy+C\)
• B. \(y.e^{\int{p_{1}dx}}=\int{(Q_{1}e^{\int{p_{1}dx}})}dx+C\)
• C. \(xe^{\int{p_{1}dy}}=\int{(Q_{1}e^{\int{p_{1}dy}})}dy+C\)
• D. \(xe^{\int{p_{1}dx}}=\int{(Q_{1}e^{\int{p_{1}dx}})}dx+C\)

Answer 1

The Correct Option is C

The integrating factor of the given differential equation \(\frac{dx}{dy}+p_{1}x=Q_{1}\) is \(e^{∫p_{1}dy}.\)

The general solution of the differential equation is given by,

\(x(I.F.)=\)\(\int{(Q×I.F.)dy}+C\)

\(⇒x.e^{\int{p_{1}dy}}=\)\(\int{(Q_{1}e^{\int{p_{1}dy)}}dy}+C\)

Hence, the correct answer is C.