Consider a physical system, the behaviour of which is captured using the following time-varying differential equation. d'x dt2 + kx= =0 is a positive real number. Let (t) be the general solution of this equation. Here, t denotes time. It is known that I(0) = A and &(0) = 0. A is a positive real number. let I be the minimum positive time such that r(T) = 0. then T is of the form: B (1. 1) T = Vab (AK) Here, a, b and care positive integers. Compute a + b + c. Define I (a) = / sin(a x? ) sin(=) x zdx If the above expression can also be written in the form I(a) = (eBa + sin(Ca) - cos(Da)), where A, B, C and D are all integers. Find A + B + C+ D An ellipse with a semi-major axis of 5 units and a semi-minor axis of 3 units, is positioned and oriented such that it is tangent to two rays. The first ray is the positive half of the x-axis, while the second ray is half of the line y = -, with