If y={"log"(x+sqrt(x^2+1))}^2,"show tha...

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

AI Generated Solution

FUNCTION
RD SHARMA ENGLISH|Exercise All Questions|406 Videos
INCREASING AND DECREASING FUNCTION
RD SHARMA ENGLISH|Exercise All Questions|232 Videos

Similar Questions

Explore conceptually related problems

If y=(x+sqrt(1+x^2))^n , then show that (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=n^2y

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=(x+sqrt(1+x^2))^n then (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)

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

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=(sin^(-1)x)/(sqrt(1-x^2)) , show that (1-x^2)(d^2y)/(dx^2)-3x(dy)/(dx)-y=0 .

If y=tan^(-1)x , show that (1+x^2)(d^2y)/(dx^2)+2x(dy)/(dx)=0 .

If y=sin^(-1)x , show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0 .

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2 .

If y=e^"tan"^((-1)"x")), prove that (1+x^2)y2+(2x-1)y1=0.
Text Solution
|
If y=(sin^(-1)x)^2 ,prove that (1-x^2)y2-x y1-2=0.
Text Solution
|
If y={"log"(x+sqrt(x^2+1))}^2,"show that"(1+x^2)(d^2y)/(dx^2)+x(dy)/(...
Text Solution
|
If x=sin(1/alogy),"show that"(1-x^2)y2-xy1-a^2y=0.
Text Solution
|
If y=x+tan x, show that cos^2 x (d^2y)/(dx^2)-2y+2x=0
Text Solution
|
If y=e^-x cos x, show that (d^2y)/(dx^2)= 2e^-x sin x
Text Solution
|
If y=log(sinx),"p r o v et h a t"(d^3)/(dx^3)=2cosxcos e c^3xdot
Text Solution
|
If y=x^3logx ,"prove that"(d^4y)/(dx^4)=6/xdot
Text Solution
|
If y=(logx)/x ,show\ tha t(d^2y)/(dx^2)=(2logx-3)/(x^3)
Text Solution
|
If y=2 sin x+3cos x, show that (d^2y)/(dx^2)+y=0
Text Solution
|
Find . (d^2y)/(dx^2),ifx=a t^2,y=2a t.
Text Solution
|
If x=sin theta,y=cosptheta,p rov e \ t h a t (1-x^2)y2-x y1+p^2y=0,w ...
Text Solution
|
If y=tan^-1x find (d^2y)/(dx^2) in terms of y alone.
Text Solution
|
If x^m y^n=(x+y)^(m+n), prove that (d^2y)/(dx^2)=0
Text Solution
|
If y^3-y=2x ,p rov et h a t(d^2y)/(dx^2)=(-24 y)/((3y^2-1)^3)
Text Solution
|
If y=x^x ,f i n d \ (d^2y)/(dx^2)
Text Solution
|
If y=sin^(-1)x , \ s how \ t h a t \ (d^2y)/(dx^2)=x/((1-x^2)^(3/2))
Text Solution
|
If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0
Text Solution
|
If y=tanx+secx ,p rov e \ t h a t \ (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)
Text Solution
|
If y=(a x+b)/(x^2+c), then (2x y1+y) y3=
Text Solution
|