Microsoft Word - Forth Exam- MATH 282- Differential Equation Instructor: Dr. Giro Carbone Fourth Exam MATH 282 Differential Equations, Spring 2021 Show all your work, Total number points = 75 you need...

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Microsoft Word - Forth Exam- MATH 282- Differential Equation Instructor: Dr. Giro Carbone Fourth Exam MATH 282 Differential Equations, Spring 2021 Show all your work, Total number points = 75 you need to get 68 or above for an A. MATH 282 Spring 2021, Dr. G. Carbone, Student’s Name__________________ 1 1) Find the Laplace Transform for the following (15 points, 5 points each): a) b) c) MATH 282 Spring 2021, Dr. G. Carbone, Student’s Name__________________ 2 2) Find the Inverse Laplace Transform for the following (15 points, 5 points each): a) b) c) MATH 282 Spring 2021, Dr. G. Carbone, Student’s Name__________________ 3 3) Solve the given Initial Value Problem by the Method of Laplace Transforms (15 points). 55 , (0) 3ty y e y    MATH 282 Spring 2021, Dr. G. Carbone, Student’s Name__________________ 4 4) Find the general solution for the given system of differential equations (15 points). 2 3 6 5 dx x y dt dy x y dt     MATH 282 Spring 2021, Dr. G. Carbone, Student’s Name__________________ 5 5) A spring/mass system is initially at rest and in its equilibrium position. The mass is 0.5 slugs and the spring constant 4 lbs/ft. At time, , the mass is struck with a force of 8 lbs for a very short period of time. The striking of the mass can be modelled using the Dirac Delta Function. Find for a damping force that is numerically equal to twice the velocity (15 points). Use the method of Laplace Transforms.