Home
Class 12
MATHS
If y=log\ [x+sqrt(x^2+1)] , prove that (...

If `y=log\ [x+sqrt(x^2+1)]` , prove that `(x^2+1)(d^2\ y)/(dx^2)+x(dy)/(dx)=0`

Text Solution

AI Generated Solution

To prove that \((x^2 + 1) \frac{d^2y}{dx^2} + x \frac{dy}{dx} = 0\) given \(y = \log\left[x + \sqrt{x^2 + 1}\right]\), we will follow these steps: ### Step 1: Differentiate \(y\) with respect to \(x\) We start with the function: \[ y = \log\left[x + \sqrt{x^2 + 1}\right] \] ...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Try youself|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise Assignment ( section -A)|61 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

  • DETERMINANTS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J|12 Videos

Similar Questions

Explore conceptually related problems

If y=log{x+ sqrt( x^2+a^2 )} , prove that: (x^2+a^2)(d^2y)/(dx^2)+x(dy)/(dx)=0 .

If y=log[x+sqrt(x^2+a^2)\ ] , show that (x^2+a^2)(d^2\ y)/(dx^2)+x(dy)/(dx)=0

If y={log(x+sqrt(x^2+1))}^2 , show that (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=2 .

If y=sqrt(x+1)- sqrt(x-1) , prove that (x^(2)-1)(d^(2)y)/(dx^(2))+x(dy)/(dx)-(y)/(4)=0

If y=sin(logx) , prove that x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 .

If y=[x+sqrt(x^2-1)]^(15)+[x-sqrt(x^2-1)]^(15) then prove that (x^2-1)(d^2y)/(dx^2)+x(dy)/(dx)-225y=0

If y={"log"(x+sqrt(x^2+1))}^2,"show that"(1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=2.

If x=sint ,y=sinpt , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.

If y="sin"(logx), then prove that (x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0

(i) If y^(1//m) + y^(-1//m) = 2x , then prove that (x^(2)-1) (d^(2)y)/(dx^(2)) + x (dy)/(dx) - m^(2)y =0 (ii) If y = ln (x + sqrt(1+x^(2))) , then prove that (1+x^(2)) (d^(2)y)/(dx^(2)) + x (dy)/(dx)=0