The general solution of a differential equation of the type is

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

14. The general solution of a differential equation of the type `

\frac{d x}{d y}+\mathrm{P}_{1} x=\mathrm{Q}_{1}

` is (A) `

y e^{\int \mathrm{P}_{1} d y}=\int\left(\mathrm{Q}_{1} e^{\int \mathrm{P}_{1} d y}\right) d y+\mathrm{C}

` (B) `

y \cdot e^{\int \mathrm{P}_{1} d x}=\int\left(\mathrm{Q}_{1} e^{\int \mathrm{P}_{1} d x}\right) d x+\mathrm{C}

` (C) `

x e^{\int \mathrm{P}_{1} d y}=\int\left(\mathrm{Q}_{1} e^{\int \mathrm{P}_{1} d y}\right) d y+\mathrm{C}

` (D) `

x e^{\int \mathrm{P}_{1} d x}=\int\left(\mathrm{Q}_{1} e^{\int \mathrm{P}_{1} d x}\right) d x+\mathrm{C}