Integrating factor of linear differential equation ` x(dy)/(dx) + 2y = x^(2) log x ` is

Options

A. `1/x^(2)`
B. `1/x`
C. x
D. `x^(2)`

Answer

D

Explanation

Given differential equation is ,
` x * (dy)/(dx) + 2y = x^(2) log x `
` :. (dy)/(dx) + (2/x) y = x * log x`
Comparing with ` (dy)/(dx) + P * y = Q `, we get
` P = 2/x , Q = x log x `
We have, ` I.F. = e^(fP*dx)`
` = e^(f2/x*dx) `
` = e^(2*f 1/x * dx) `
` = e^(2*log x) = e^(log x^(2) = x^(2)`.
Hence, the correct answer from the given alternatives is (d).