M340 Differential Equations Final Exam - Prof. Travis A. Olson, Exams of Differential Equations

Download M340 Differential Equations Final Exam - Prof. Travis A. Olson and more Exams Differential Equations in PDF only on Docsity! M340 Differential Equations Final NAME: P#1 10 P#2 10 P#3 10 P#4 10 P#5 10 Total 50 WARNING: A calculator is allowed as well as the note sheets I distributed from test 1, test 2 and the final. If additional space is needed, write your name on every page submitted, and staple them to your exam. Show your work and circle your answers. Mathematics 340 2 Question 1. Solve the following initial value problem: y′ = t(y + 2), y(0) = 0. Mathematics 340 5 Question 4. Find the general solution to the following second order differen- tial equation. y′′ + 9y = 9e3t Mathematics 340 6 Question 5. Use Laplace transforms to solve the following initial value prob- lem. y′′ − 4y′ + 4y = e2t, y(0) = 1, y′(0) = 2 Table of Laplace Transforms f(t) for t ≥ 0 L(f) 1 1 s eat 1 s− a tk−1 (k−1)!e at 1 (s− a)k tn n! sn+1 (n = 0, 1, . . .) sin at a s2 + a2 cos at s s2 + a2 y′(t) sY (s)− y(0) y′′(t) s2Y (s)− sy(0)− y′(0)