Question 3 a) What conditions on the functions g(t) and h(t) must be satisfied for the differential equation to be exact? b) What is the solution of the differential equation in a) when these conditions are satisfied? Solve the initial value problem dx (1 + cos² t). g(t)- +h(t)x=0 dx dt dt x sin 2t = 4t² + 2t + 3, x(0) = 2

Question 3 a) What conditions on the functions g(t) and h(t) must be satisfied for the differential equation to be exact? b) What is the solution of the differential equation in a) when these conditions are satisfied? Solve the initial value problem dx (1 + cos² t). g(t)- +h(t)x=0 dx dt dt x sin 2t = 4t² + 2t + 3, x(0) = 2