The function satisfying the equation f(x)=- _ 0 ^ x f(t) t d t+ _ 0 ^ x (t-x) d t, where…
Mathematics · JEE Advanced · NTA Exams — Differential Equations
The function satisfying the equation
\(f(x)=-\int_{0}^{x} f(t) \tan t d t+\int_{0}^{x} \tan (t-x) d t,\)
where \(\mathrm{x} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)is :
\(f(x)=-\int_{0}^{x} f(t) \tan t d t+\int_{0}^{x} \tan (t-x) d t,\)
where \(\mathrm{x} \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)is :
- 1 + cos x
- 1 – cos x
- cos x – 1
- none
Answer
(C) cos x – 1
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- The Explanation:tion of the differential equation (x 3 – 3xy 2 ) dx = (y 3 – 3x 2 y) dy is
- Explanation:tions of the differential equation ( d y d x )^ 2 - d y d x (e^ x +e^ -x )+1=0 are given by
- If _ a ^ x t y(t) d t = x 2 + y (x) then y as a function of x is
- The x-intercept of the tangent to a curve is equal to the ordinate of the point of contact. The equation of…
- Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known…
- Let a solution y = y ( x ) of the differential equation x x^ 2 -1 d y-y y^ 2 -1 d x=0 satisfies y(2)= 2 3 …
- Let f : [0, ∞) → be a continuous function such that f(x)=1-2 x+ _ 0 ^ x e^ x-t f(t) d t for all x ∈[0, ∞)…
- The solution of primitive equation ( x 2 + y 2 ) dy = xy dx , is y = y ( x ). If y (1) = 1 and y ( x 0 ) = e…
More Differential Equations questions · Browse all practice questions