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MA 2051 D '97 Sample Exam 1
Show your work in the space provided. Unsupported answers may not
receive full credit.
- Explain what it means for a function u to be a solution of the
DE y' = f(x,y) on an interval .
- Consider the following differential equation.
- Use the method of characteristics to find the general solution of the
corresponding homogeneous equation.
- Find a particular solution, using the method of undetermined
- Find a solution that satisfies the initial condition y(-1)=5.
- Consider the differential equation
- Is this DE linear? Explain why or why not.
- Use separation of variables to solve the corresponding
homogeneous differential equation. For which values of x does your
solution make sense?
- Use variation of parameters to find the general solution to the
- Can you find a solution that satisfies the initial condition
y(0)=2? If your answer is yes, give your solution. If your answer is
no, explain what goes wrong.
- Imagine that you were trapped at home during the recent
blizzard. Unfortunately, you were unlucky enough to lose power. You
are well-prepared, however, with a supply of candles and fuel for your
- Derive a model to describe the temperature in your house,
assuming the temperature outside is constant at and that the
stove generates heat at a constant rate Q in units of energy per
- Solve the differential equation you derived above for the
initial condition .
- Explain the qualitative behavior of your model.
William W. Farr
Fri Apr 4 09:08:00 EST 1997