Find the general solution of the following differential equation: d²x 1 dx dt² The given ODE satisfies x(1) Hints: + = t² (x) ¹, t dt = 2 and (1) 1. Note that = = dx dt • Classify the ODE and make preliminary analysis for it. The given ODE in this question can be solved using the knowledge you have gained so far, especially Topics 3 and 5.

Please answer the point a

Given the differential equation below, find the solution using Laplace transformation. The parameters R, C, and V, are constants that are related to the resistance and the capacitance in an RC circuit which is discharging. Vc is the function you have to solve for and it corresponds to the voltage across the capacitor. Initially Vc (0) Vo. RC dvc + Vc = 0 (a) Give an expression for Vc(s), where L{Vc(t)} = Vc(s), (b) Give an expression for Vc(t); the solution to the differential equation

Question 3 part D