Math2306 Exam 4 Review Problems: Laplace Transforms - Prof. Taixi Xu, Exams of Differential Equations

Download Math2306 Exam 4 Review Problems: Laplace Transforms - Prof. Taixi Xu and more Exams Differential Equations in PDF only on Docsity! Math2306 Review Problems for Exam 4 (Covers Chapter 7) 1. Use definition to find the Laplace transform )}({ tfL . a)       11 10,1 )( t t tf b)       11 10, )( t tt tf 2. Use formulas to find the Laplace transform )}({ tfL . a) 52)( 4  ttf b) tetf 31)(  c) tttf 5sin42cos3)(  3. Find the given inverse Laplace transform. a)         2 11 s L b)         2 1 2 1 s s L c)         )2)(2( 11 sss L d)         )2)(2( 2 1 ss s L e)         22 1 )2( 1 ss L 4. Use the Laplace transform to solve the given initial-value problems. a) 2)0(,6 4  yeyy t b) 0)0(,5cos2  ytyy c) 5)0(,0)0(,2  yyeyyy t d) 1)0(,0)0(,0)0(,2332   yyyeyyyy t e) 0)0(,10)0(,2sin2  yytyy 5. Use formulas to find the Laplace transform )}({ tfL . a) ttetf 6)(  b) tetf t 4cos)( 2 c) ) 2 sin1049()( 3 t tetf t  6. Find the given inverse Laplace transform. a)         4 1 )1( 1 s L 1