Home
Class 12
MATHS
If y = (tan^-1 x)^2, then prove that (1+...

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

Promotional Banner

Similar Questions

Explore conceptually related problems

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

If y = e^(3tan^-1 x) , then show that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^2)dy/dx = 9y

If y = e^(4tan^-1 x) , then show that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^2)dy/dx = 16y

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

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

If y = e^(3tan^-1x) , then show that : (1 + x^2)^2 d^2y/dx^2 + 2x ( l +x^2 ) dy/dx= 9y .

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

If y = e^(4xtan^-1x) , then show that : (1 + x^2)^2 d^2y/dx^2 + 2x ( l +x^2 ) dy/dx= 16y .

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