Home
Class 12
MATHS
If y=e^(2tan^(-1)x), the show that : (1...

If `y=e^(2tan^(-1)x)`, the show that : `(1+x^(2))^(2)(d^(2)y)/(dx^(2))+2x(1+x^(2))dy/dx=4y`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE 5(a) (SHORT ANSWER TYPE QUESTIONS)|52 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE 5(a) (LONG ANSWER TYPE QUESTIONS (I))|39 Videos
  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos
  • DETERMINANTS

    MODERN PUBLICATION|Exercise Chapter test 4|12 Videos

Similar Questions

Explore conceptually related problems

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

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

If y=asin^(-1)x , then show that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0

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

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

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

If y=(tan^(-1)x)^(2), then (x^(2)+1)^(2)(d^(2)y)/(dx^(2))+2x(x^(2)+1)(dy)/(dx)=

If y=cos^(-1)x , then show that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx=0

If y=e^(mtan^(-1)x) , prove that : (1+x^(2))(d^(2)y)/(dx^(2))+(2x-m)dy/dx=0 .

If y=e^(a cos^(-1)x),-1<=x<=1 then show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-a^(2)y=0