Consider a physical system, the behaviour of which is captured using the following time-varying differential equation. d'x dt2 7+ ke' =0 k is a positive real number. Let a(t) be the general solution of this equation. Here, t denotes time. It is known that x(0) = A and i(0) = 0. A is a positive real number. let T 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 c are positive integers. Compute a + b + c. Define I (a) - sin(a x?) sin(=2) x 2dx If the above expression can also be written in the form I(a) = = (eBo + 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 = -r, with r