In each case, solve the dierential equation (or initial value problem). Note that the general solution to a second-order dierential equation should have two arbitrary constants.

Question 4. [1+ (3+3+3+3) marks] In each case, solve the differential equation (or initial value problem). Note that the general solution to a second-order differential equation should have two arbitrary constants. (a) y' = y(1+x3) (b) xy' + 2y = 4x2, y(1) = 2 (c) dy = sec(y) tan(y), y(0) = 0, y'(0) = 1 Hint: Plug in the initial conditions when you get to an equation that only in- volves y and dy/dx, to make the later steps easier. (d) xy" + 2y' = 12.2