Problem B.7 Consider the ODE v+ P{x)y = [(x). If P{x) and f{x) are both constants, then the ODE can be solved by separation of variables. Suppose P(x) = a and f(x) = b, where a and b are non-zero constants, We then have the ODE + ay = b. If y({0) = , solve the nitial-value problem. Verify by substitution that the explicit solution satisfies the ODE. Problem B.3 1-order linear homogengous ODEs having one dependent variable are of the form ::+ Pix)y = 0. Use the method of separation of variables to show that their general solution is of the form vy = ce S Pixdx