" If "y=ax^(n+1)+bx^(-n)" then "x^(2)y_(2)=dots dots

If y=ax^(n+1)+bx^(-n), then x^(2)(d^(2)y)/(dx^(2))=n(n-1)y(b)n(n+1)y(c)ny(d)n^(2)y

If y=ax^(n+1)+bx^(-n), then x^(2)(d^(2)y)/(dx^(2)) is equal to n(n-1)y(b)n(n+1)yny(d)n^(2)y

If y = ax^(n+1)+bx^(n+1) then x^2(d^2y)/(dx^2) is equal to

If y = ax^(n+1) + bx^(-1) , then x^(2) (d^(2)y)/(dx^(2)) =

If y=ax^(n+1)+bx^(-n) then show that x^(2)y''=n(n+1)y .

If y=ax^(n+1)+bx^(-n) and x^(2)(d^(2)y)/(dx^(2))=lambda y then write the value of lambda.

If y = e^(ax) cos bx then find y_(n)(0) .

If y^(2)=ax^(2)+2bx+c and u_(n)= int (x^(n))/(y)dx , prove that (n+1)a u_(n+1)+(2n+1)bu_(n)+(n)c u_(n-1)=x^(n)y and deduce that au_(1)=y-b u_(0), 2a^(2)u_(2)=y(ax-3b)-(ac-3b^(2))u_(0) .

If y^(2)=ax^(2)+2bx+c , and u_(n)= int (x^(n))/(y)dx , prove that (n+1)a u_(n+1)+(2n+1)bu_(n)+(n)c u_(n-1)=x^(n)y and deduce that au_(1)=y-b u_(0), 2a^(2)u_(2)=y(ax-3b)-(ac-3b^(2))u_(0) .