test2-1 - . Answer: characteristic polynomial is , with...

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MATH 315 FALL 2006 TEST 2 KEY 1. (20 pts.) Consider the differential equation . 1. Find the general solution for the equation. Answer: characteristic polynomial is , with roots 0, -1, 2. The general solution is therefore 2. Determine the Wronskian for your fundamental solution set. 3. Determine the solution that satisfies initial conditions , , . the solution to the linear system is , , . Final solution:
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2. (16 pts.) Find the general solution for the differential equation . Answer: characteristic polynomial is , with roots , so A particular solution should have the form Final solution: . 3. (15 pts.) Suppose the general solution to a order homogeneous equation is Determine the general form that would be used with the method of undetermined coefficients for the solution to the nonhomogeneous equation
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Final solution: 4. (23 pts.) Find the general solution for the differential equation
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Unformatted text preview: . Answer: characteristic polynomial is , with roots , so . For , a particular solution should have the form Comparing terms, , , . For , a particular solution should have the form Final solution: 5. (6 pts.) Determine intervals where the solution for the following problem is sure to exist: Answer: the equation in standard form is , so the coefficient functions for and , and the function do not exist when . There should be a unique solution when or or . 6. (20 pts.) Use the variation of parameters method to solve the differential equation with initial values , and . Answer: characteristic polynomial is , with roots . , so The linear system is , . Adding first equation to second equation , the result is , so and ; using first equation, , so . Therefore ; now , and , so and . Final solution: ....
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This test prep was uploaded on 04/06/2008 for the course MATH 302 taught by Professor Goldberg during the Spring '08 term at Johns Hopkins.

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test2-1 - . Answer: characteristic polynomial is , with...

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