TEST3/MAP2302 Page 4 of 4 ______________________________________________________________________ 8. (15 pts.) Using only the Laplace transform machine, solve the following first order initial-value problem. By taking the Laplace Transform of both sides of the differential equation, and using the initial condition, we have By taking inverse transforms now, we quickly obtain ______________________________________________________________________ 9. (10 pts.) The solution to a certain linear ordinary differential equation with coefficient functions analytic at x0 = 0 is of the form where the coefficients satisfy the following equations: Determine the exact numerical value of the coefficients c0 , c 1 , c 2 , c 3 , and c 4 for the particular solution that satisfies the initial conditions y (0) = -2 and y ′ (0) = 1. ______________________________________________________________________ 10 Point Bonus ? : (a) With proof, give an example of an initial-value problem at x0 = 0 with a nonzero solution and the ODE linear homogeneous of 1 st order, such that the Laplace transform of the IVP is a linear ODE of 2 nd order. (b) Provide the solution to the un-transformed 1 st order IVP. [Say where your work is below, for there isn’t room for your work here. See de-t3-bo.pdf. ]
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