Home
Class 12
MATHS
If y=[x+sqrt(x^2-1)]^(15)+[x-sqrt(x^2-1...

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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MODEL TEST PAPER - 4

    ICSE|Exercise SECTION - B|10 Videos

  • MODEL TEST PAPER - 4

    ICSE|Exercise SECTION - C|10 Videos

  • MODEL TEST PAPER - 3

    ICSE|Exercise SECTION - C|10 Videos

  • MODEL TEST PAPER - 7

    ICSE|Exercise Section - C |5 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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=e^(tan^(-1)x) then prove that : (1+x^(2))(d^2y)/(dx^2)+(2x-1)(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=xln((a x)^(-1)+a^(-1)) prove that x(x+1)(d^2y)/(dx^2)+(dy)/(dx)=y-1