Question

The integrating factor of differential equation `R(dx)/(dy) + Px = Q`, where P, Q, R are functions of y, is ______.

विकल्प

• `e^(intP/Qdy)`

• `e^(intPdy)`

• `e^(intP/Rdy)`

• `e^(intP/Rdx)`

Answer 1

The integrating factor of differential equation `R(dx)/(dy) + Px = Q`, where P, Q, R are functions of y, is `underlinebb(e^(intP/Rdy))`.

Explanation:

Given `R(dx)/(dy) + Px = Q`,

Divide by `R: (dx)/(dy) + P/Rx = Q/R`

A linear equation in x. The integrating factor is `e^(intP/Rdy)`, obtained from standard form `(dx)/(dy) + Pyx = Qy`.