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 coefficients.
- 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 differential equation.
- 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
wood stove.
- 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 unit time. - Solve the differential equation you derived above for the initial condition .
- Explain the qualitative behavior of your model.

- 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

Fri Apr 4 09:08:00 EST 1997