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) `x e^(intP_1dx)

Options

A. `y*e^(intP_(1)dy)=int(Q_(1)e^(intP_(1)dy))dy+C`
B. `y*e^(intP_(1)dx)=int(Q_(1)e^(intP_(1)dx))dx+C`
C. `x*e^(intP_(1)dy)=int(Q_(1)e^(intP_(1)dy))dy+C`
D. `x*e^(intP_(1)dx)=int(Q_(1)e^(intP_(1)dx))dx+C`

Explanation

The intergrating factor of the given differential equation `(dx)/(dy)+P_(1)x=Q_(1)` is `e^(intP_(1)dy)`
Thus, the general solution is : `x*I.E.=int(QxxI.E.)dy+c`
`:. Xe^(intP_(1)dy)=int(q_(1)e^(intP_(1)dy))dy+c`