Home
Class 12
MATHS
If y=sqrt(x+1)- sqrt(x-1), prove that (x...

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

Promotional Banner

Topper's Solved these Questions

  • MODEL TEST PAPER-16

    ICSE|Exercise SECTION -B (65 MARKS)|10 Videos
  • MODEL TEST PAPER-16

    ICSE|Exercise SECTION -C (65 MARKS)|10 Videos
  • MODEL TEST PAPER-12

    ICSE|Exercise SECTION-C |10 Videos
  • MODEL TEST PAPER-5

    ICSE|Exercise Section -C|10 Videos

Similar Questions

Explore conceptually related problems

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

If y=e^("mcos"^(-1)x) , prove that: (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=m^(2)y

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

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+a^2 )} , prove that: (x^2+a^2)(d^2y)/(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=x^(x) , prove that: (d^(2)y)/(dx^(2))-1/y((dy)/(dx))^(2) - y/x=0