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MATH 245 1. (25 points) Solve y" +9y=0. y(0) = 1, y(0)=3 2 SFSU
DIRECTION: The EXAM 2 is on FRIDAY, JULY 8 FROM 9:00AM - 10:00AM. Students are allowed extra 15 mins to take the picture or scan your completed exam and upload/ paste on iLearn in PDF file by 10:15AM of JULY 8, 2022. You will get ZERO for the EXAM if you upload your exam after 10:15AM OR your completed exam is NOT in ONE PDF file (ONE PDF FILE CAN HAVE MULTIPLE PAGES). Don't forget to write your name on your exam paper before you scan or take picture. For full credit, use proper notation, show how results are obtained, and present results in simplified form. There are some case you get 0 credit for a problem: 1) You DO NOT show your work how to get the answer. 2) You do steps wrongly but still get the right answer. 3) You skip some important steps and jump to the answer. IMPORTANT NOTE: YOU MUST DO THE EXAM BY YOURSELF. Laplace table: Inverse Laplace table: f(t) eat f(t) sin at cos at y (t) y"(t) F(s) = L[ƒ(t)] n!/8"+1 F(s) 1/sn F(s-a) 1/(s² + a²) s/(s² + a²) F(s-a) a/(s² + a²) 8/(8²+ a²) SY (s)-y(0) s²Y(s) — sy(0) — y′(0) f(t)=L¹[F(s)] t"-¹/(n-1)! eat f(t) (1/a) sin at cos at
MATH 245 2. (25 points) Use method of undetermined coefficients. y"-2y +2y=2x-2. 3 SFSU
3. (25 points) Use method of variation of parameters. y"+2y-8y=2e-2x - e-x.
4. a) (10 points) Find the Laplace of f(t)=(t-2)(t+2)e-3r b) (15 points) Find the Inverse Laplace of F(s) 5 $+3 (S-2)³