Unformatted text preview: Problems 1-4 1. Verify that is a solution of for all and for all constant and . 2. By integrating times, find the general solution of 3. For what values of does determine as a differentiable function of x which satisfies ? 4. Find the values of , if any, for which is a solution of: a. b. c. 5. Find the values of for which is a solution of 6. Assume that the implicit function determines interval. Without attempting to solve the equation for equation as a differentiable function of x in some , show that satisfies the differential 7. a. Define what should be meant by a solution of the partial differential equation b. Show that is a solution of this equation provided twice-differentiable functions. Hint: Use the chain rule: and are 8. Find the values of a, b and w for which is a solution of the system of equations Answers and Hints 3. 4. a. c. 5. 8. arbitraray b. No value. ...
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- Fall '11
- Derivative, Partial differential equation, differentiable function