Question

Solve the linear PDE, p+q = 2xy​

Answer 1

Answer:

Correct option is

B

x(I.F)=∫(I.F.)Qdy+C

Consider the differential equation of type

dydx+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

d(xe.∫P(y)dy)=e∫P(y)dyQ(y).dy

∫d(xe.∫P(y)dy)=∫e∫P(y)dyQ(y).dy

xe.∫P(y)dy=∫e∫P(y)dyQ(y).dy

x.IF=∫IFQ(y).dy+C