If y = etan^-1 x, show that (1 + x2) y” + (2x – 1) y’ = 0 – InterviewSolution

1.

If y = etan^-1 x, show that (1 + x2) y” + (2x – 1) y’ = 0

Answer»

y = e^{tan^-1 x}

y = e^{tan^-1 x} 1/(1 + x²)

⇒ y’ = y/(1 + x²) ⇒ y'(1 + x²) = y

Differentiating w.r.to x

y’ (2x) + (1 + x²) (y”) = y’

(i.e.) (1 + x²) y” + y’ (2x) – y’ = 0

(i.e.) (1 + x²) y” + (2x – 1) y’ = 0

Discussion

No Comment Found

Related InterviewSolutions

Write an example of a function which is everywhere continuous but fails to be differentiable exactly at five points.
It is given that f'(a) exists, then \(\lim\limits_{x \to a} \frac{xf(a)-af(x)}{x-a}\) is …(a) f(a) – af'(a) (b) f ‘(a) (c) -f ‘(a) (d) f(a) + af ‘(a)
The derivative of f(x) = x|x| at x = -3 is …(a) 6 (b) -6 (c) does not exist (d) 0
If f(x) = x + 2, then f'(f(x)) at x = 4 is …(a) 8 (b) 1 (c) 4 (d) 5
If y = mx + c and f(0) = f'(0) = 1, then f(2) is …(a) 1 (b) 2 (c) 3 (d) -3
Find the derivatives of the function with respect to corresponding independent variables.y = ex sin x
Find the derivatives of the function with respect to corresponding independent variables.(i) y = cos x – 2 tan x(ii) g(t) = t3 cos t
Find the derivatives of the function with respect to corresponding independent variables.g(t) = 4 sec t + tan t
Find the derivatives of the function with respect to corresponding independent variables.(i) y = sin x + cos x(ii) f(x) = x sin x
Find the derivatives of the function with respect to corresponding independent variables. f(x) = x – 3 sin x