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Study Guide for Final

# Study Guide for Final - M341 Study Guide for the Final(S...

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M341 Study Guide for the Final (S. Zhang) . 1. Determine if the existence and uniqueness theorem for the first order DE guarantee the solution (in a neighborhood) for each of the initial value problems: ( a ) dy dx = y 1 / 3 ; y (0) = 0 ( b ) dy dx = y 1 / 3 ; y (1) = 0 ( c ) dy dx = y 1 / 3 ; y (0) = 1 (show your work.) 2. Find the general solution of dy dx + 2 xy 2 = 0 3. A cake is removed from an oven at 210 0 F and left to cool at room temperature, which is 70 0 F. After 30 min the temperature of the cake is 140 0 F. When will it be 100 0 F? 4. Solve the DE by regarding y as the independent variable. ( x + ye y ) dy dx = 1 5. Suppose that when a certain lake is stocked with fish, the birth and death rates β and δ are both proportional to 1 / P . If P 0 = 900 and after 6 months, there are 441 fish in the lake, how long did it take all the fish in the lake to die? 6. Find the general solution: y + 4 y + 4 y = 0 7. Solve y (4) + 3 y - 4 y = 0 8. Find a linear homogeneous constant-coefficient equation with the given solution.

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Study Guide for Final - M341 Study Guide for the Final(S...

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