q4 - MA366 Sathaye Quiz 4 Name Sec/Row 1 Solve the...

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Unformatted text preview: MA366 Sathaye Quiz 4 Name/ Sec./Row 1. Solve the differential equation 2y + 3y + y = 0 and write down its general solution. Now solve the above equation with initial conditions y(0) = 1, y (0) = -2. 2. Solve the differential equation y + 4y + 8y = 0 and write down its general solution. 3. Solve the differential equation y + 4y + 4y = 0 and write down its general solution. Now solve the above equation with initial conditions y(0) = 10, y (0) = 0. 1 Key 1. Solve the differential equation 2y + 3y + y = 0 and write down its general solution. Answer: Find roots of 2D2 + 3D + 1 = (2D + 1)(D + 1), so -1/2, -1. The general solution is: c1 e-t/2 + c2 e-t . Now solve the above equation with initial conditions y(0) = 1, y (0) = -2. Answer: We get two equations: c1 + c2 = 1, -(1/2)c1 - c2 = -2. The solution is c1 = -2, c2 = 3. Final answer: -2e-t/2 + 3e-t . 2. Solve the differential equation y + 4y + 8y = 0 and write down its general solution. Answer: Find roots of D2 + 4D + 8 = (D + 2)2 + 4. So -2 2i. Hence y = e-2t (c1 cos(2t) + c2 sin(2t)). 3. Solve the differential equation y + 4y + 4y = 0 and write down its general solution. Answer: Find roots of D2 + 4D + 4 = (D + 2)2 . So -2 is a double root. Hence y = e-2t (c1 + c2 t). Now solve the above equation with initial conditions y(0) = 10, y (0) = 0. Answer: We get two equations c1 = 10, c2 - 2c1 = 0. So, c1 = 10, c2 = 20. Final answer: e-2t (10 + 20t). 2 ...
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This note was uploaded on 01/18/2012 for the course MATH 366 taught by Professor Edraygoins during the Fall '09 term at Purdue.

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q4 - MA366 Sathaye Quiz 4 Name Sec/Row 1 Solve the...

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