Question

if y = axⁿ⁺² + bx^-n-1, then `x^2(d^2y)/(dx^2)` is ______.

Options

• n(n - 1)y

• (n + 1)(n + 2)y

• ny

• n²y

Answer 1

if y = axⁿ⁺² + bx^-n-1, then `x^2(d^2y)/(dx^2)` is (n + 1)(n + 2)y.

Explanation:

y = axⁿ⁺² + bx^-n-1       ....(i)

`thereforedy/dx=(n+2)ax^(n+1)-(n+1)bx^(-n-2)`

`therefore(d^2y)/(dx^2)=(n+2)(n+1)ax^n+(n+1)(n+2)bx^(-n-3)`

`=>(d^2y)/(dx^2)=((n+2)(n+1))/x^2(ax^(n+2)+bx^(-n-1))`

`=>x^2(d^2y)/dx^2=(n+1)(n+2)y`    .....[From (i)]