Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Ordinary Differential Equations
Let g : ℝ → ℝ be a continuous function. Which one of the following is the solution of the differential equation
\(\frac{d^2 y}{d x^2}+y=g(x) \text { for } x \in \mathbb{R}\),
satisfying the conditions y(0) = 0, y′(0) = 1 ?
1
\(y(x)=\sin x-\int_0^x \sin (x-t) g(t) d t\)
2
\(y(x)=\sin x+\int_0^x \sin (x-t) g(t) d t\)
3
\(y(x)=\sin x-\int_0^x \cos (x-t) g(t) d t\)
4
\(y(x)=\sin x+\int_0^x \cos (x-t) g(t) d t\)