Question

If y = x^n–1 log x, then x² y₂ + (3 – 2n) xy₁ is equal to

A. – (n – 1)² y 

B. (n – 1)² y 

C. – n²y 

D. n²y

Answer 1

Correct Answer is (A) – (n – 1)² y

Given:

y = x^n–1 log x

\(\frac{dy}{dx}\)\(=(n-1)x^{n-2}logx+\frac{1}{x}x^{n-1}\)

= (n - 1)x^n-2 logx + x^n-2

= x^n-2 [(n - 1)logx + 1]

xy₁ = x^n-1[(n - 1)logx + 1]

= (n - 1)y + x^n-1