MATH 246 Final: MATH246 BOYLE-M SUMMER I2005 0101 FINAL EXAM

• School: University of Maryland
• Department: Mathematics
• Course: MATH 246
• Professor: All

Document Summary

Put a box around the result of a computation. You are allowed one page of notes (both sides): (35 points) find the solution to the initial value problem dy dx y sec2(x) + ex. 2y + tan(x) y(0) = 2 in which y represents a real-valued function of x. Give a formula for the solution y as a function of x. **********there are more problems on the back side************: (45 points) suppose x(t) and y(t) are real-valued functions of time t, governed by the system of equations dx dt dy dt. Does the model suggest the species could coexist in a stable way: (10 points) the following system of di erential equations de nes an autonomous system in the plane in polar coordinates: dr dt. = r(r 1)(r 3) , d dt. Determine all periodic solutions and all limit cycles, and determine their stability characteristics: (15 points) for each part below, answer true or false.