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

Answer: (C)

$xe^{\int{p_{1}dy}}=\int{(Q_{1}e^{\int{p_{1}dy}})}dy+C$

Answer 2

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.