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

• 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. Rewrite the di erential equation in the form m (x, y) + n (x, y) dy dx = 0 as follows, (cid:18)y sec2(x) + ex(cid:19) +(cid:18)2y + tan(x)(cid:19) dy dx. Then m/ y = n/ x (both partial derivatives equal sec2(x)), so the d. e. is exact. Therefore there is a function h(x, y) and a constant c such that any solution has its graph contained in the set of points (x, y) where h = c. also, h/ x = m and. Andi erentiating m with respect to x (holding y constant) we see.