Homework 2, due 8 September 2005.

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Solve each of the following differential equations using the methods from chapters 2 and 3 in the course text. If the equation cannot be solved using a method from chapters 2 or 3 in the course text, the correct answer is to indicate that the equation cannot be solved using the methods from the course text. Be sure to indicate in words what method you are using for each problem.

Each problem is worth 10 points.

1. Determine the solution to
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2. Determine the solution to
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3. Determine the general solution to
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4. Determine the solution to
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5. Determine the solution to
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6. Determine the general solution to
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7. Determine the general solution to
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8. Determine the general solution to
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9. Determine the solution to
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10. Determine the solution to
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11. Determine the general solution to
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12. Assume that x1(t) and x2(t) are solutions to the following ordinary, second order differential equations. For which of the following is the linear combination of the two solutions
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    also a solution?
    1. 
    2. 
    3. 
    4. 
    What are the differences between the cases where the linear combination is a solution and the cases where it is not?