1. Show that if y1 and y2 are solutions to the second-order linear differential equation p(t)y '' + q(t)y' + r(t)y = g(t), then y := c(y1 y2) is a solution to the homogeneous equation p(t)y'' + q(t)y' + r(t)y = 0, for any real constant c
2. . Solve the initial value problem y'' + 4y' + 4y = 0, y(1) = 2, y' (1) = 1
3. Use the method of reduction of order to find a second solution y2 of the given differential equation.
4. (a) t ²y '' 4ty' + 6y = 0, (t > 0); y₁(t) = t² .