If y = a x^n+1 + bx^–n and x^2 d^2y/dx^2= λy then write the value of λ.

Question

If y = a xⁿ⁺¹ + bx^–n and \(x^2\frac{d^2y}{dx^2}=\lambda y,\) then write the value of λ.

Answer 1

Given:

y=axⁿ⁺¹ +bx^-n

λy=n(n+1)a x^n-1+2 +n(n+1)bx^-n-2+2

λy=n(n+1)[a x⁽ⁿ⁺¹⁾+bx^(-n)]

λy=n(n+1)

λ=n(n+1)