Initial value problems:
Solve the initial value problems;
1a) t(dy/dt) + 5y = 7t w/ y(1) = 3
1b) (dy/dt) + 0.1ty = 7t w/ y(0) = 4
1c) 11(t+1)(dy/dt) - 7y = 28t for t > -1 w/ y(0) = 20
1d) (dy/dt) + 2y = 25sin(t) + 30cos(t) y(0) = 1
1e) (dy/dt) + 5y = cos(4t) w/ y(0) = 0
1f) 9(dy/dt) + y = 18t w/ y(0) = 1 find y as a function of t
1g) Find the function satisfying the differential equation , f'(t) - f(t) = 4t w/ f(1) = -1
1h) Find the particular solution of the differential equation , (dy/dx) + ycos(x) = 6cos(x) w/ y(0) = 8
Provide step by step calculations.