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

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

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

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

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