9:23 B hw4.pdf - Saved Math 201-Assignment 4 Due on November 15, 2023, 5 pm where g = g(t) is a given function. 2. (10 pts) Find the inverse Laplace transform of -ja- 0 1. (10 pts) Use the convolution theorem to obtain a formula for the solu- tion to the initial value problem y"+y=g, y(0) = 0, y'(0) = 1, 3. (10 pts) Solve the integral equation y(t) + 4. Solve the following initial value problems: (a) (10 pts) y" + 5y' + 6y = e8(t-2), (b) (10 pts) x - 3x + 2y = sint, 4x - y - y = cost, ||| K 7 x + y = x, 2x +y" = u(t 3), 1 (s+1) s (tv)y(v) dv=t. 1 y(0) = 2, y'(0) = -5. x(0) = 0, y (0) = 0. x(0) = 0, y(0) = 1, y'(0) = -1. go (c) (10 pts) 5. Consider the IVP for y = y(x), y" + 2y + y = x, y(0)=y'(0) = 0. (*) (a) (5pts) Use power series in x to solve (*); compute the first four nonzero terms of the series. (b) (5 pts) Find the solution y of (*) using the method of undeter- mined coefficients. Determine the Taylor series of y about to = 0. Is this the same series as in (a)? 6. (10 pts) Find the first four nonzero terms in the power series solution about to 0 to y" + (x 2)y' - y = 0, y(0) = -1, y'(0) = 0. ll 100% 8. (10 pts) Find the first four nonzero terms of the solution to y"+ty' + et y = 0, y(0) = 0, y'(0) = 7. (10 pts) Find a lower bound for the radius of convergence of the power series solution about xo = 1 to (1+x)y" xy' + 3xy = 0. = -1.