Consider a physical system, the behaviour of which is captured using the following time-varying differential equation. d'x dt? + 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 a(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. ) T = Vab ( AK) Here, a, b and care positive integers. Compute a + b + c. 1 " sinla z ? ) sin ( = 1 x do If the above expression can also be written in the form I(a) = (eBe + 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