The solution of a linear differential equation dxdy+Px=Q where P and Q are functions of y, is:
A
y(I.F)=∫(I.F.)Qdx+C
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B
x(I.F)=∫(I.F.)Qdy+C
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C
y(I.F)=∫(I.F.)Qdy+C
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D
x(I.F)=∫(I.F.)Qdx+C
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Solution
The correct option is Bx(I.F)=∫(I.F.)Qdy+C Consider the differential equation of type dxdy+P(y)x=Q(y) Then, the integrating factor for the above integral is I.F=e∫P(y).dy Hence multiplying the above integral by I.F e∫P(y)dy.dx+P(y)xe∫P(y)dy.dy=e∫P(y)dyQ(y).dy