Question

1. (a) Solve y′ = 9.8 – 0.196y
(b) Solve the initial value problem y′ = e^(-x), y(0) = 2.
(c) Solve the initial value problem y′ = e^(-x) y^2, y(1) = 4.

2. (a) Solve the differential equation y′ + 1/x y = 3x^2y^3 , which is nonlinear.
(b) An amoeba population has an initial size of 1000. It is observed that , on every ten amoeba reproduce by cell division every hour. Find the approximate size of the amoeba population in 30 hours.

3. (a) Find the general solution to the following differential equation
y′′ + 4y = secx, -π/4 < x < π/4
(b) Find the particular solution to
ty′′ - (t + 1)y′ + y = t2 given that y1(t) = et, y2(t) = t + 1 form a fundamental set of solutions for the homogenous differential equation.