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The general solution of a differential ...

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`

Text Solution

Verified by Experts

Given DE is` dx/(dy)​+P1​x=Q1`​
which is an exact DE, thus the integrating factor is given by
`IF=e^(∫P1)​ dy`
General solution of this DE is given by
`x e^(∫P1​)dy=∫(Q1​ e^(∫P1​)dy)dy+C`
So,Correct option is C
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