The general solution of a differential equation of the type `(dx)/(dy)+P_1x=Q_1` is (A) `y e^(intP_1dy)=int(Q_1e^(intP_1dy))dy+C` (B) `ydote^(intP_1dx)=int(Q_1e^(intP_1dx))dx+C` (C) `x e^(intP_1dy)=int(Q_1e^(intP_1dy))dy+C` (D) `xe^(intp_1dx)=intQ_1e^(intp_1dx)dx +C`

Explanation

Given ,` d x / d y+P_{1} x=Q_{1}`


To solving this equation we have tp multiply each side sides by


Integrating factor =`I . F.=e^{p_1dy}}`


Then ,`e^{int A d y}(frac{d x}{d y}+P_{1} x)=Q_{1} e^{int p_1 d y}`



`Rightarrow frac{d x}{d y} e^{int cap d y}+P_{1} e^{int R d y}=Q_{1} e^{int P_1 d y} `

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Rightarrow frac{d}{d y}(x e^{int R d y})=Q_{1} e^{int R d y} `

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Rightarrow int frac{d}{d y}(x e^{int R d y}) d y=int Q_{1} e^{int P_1 d y} d y `

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