MATH 0290 Midterm: Math 0290 Exam 1 (0290) 2016 Fall Solution -187
Document Summary
1. (a) (15 points) solve the initial value problem x = 1 + x tan t, x(0) = 5. Solution: x (tan t) x = 1. The integrating factor is u = e r tan t dt = eln(cos t) = cos t. sin t cos t (note: r tan t dt = r. Then (cos t) x (sin t) x = cos t, Therefore, x(t) = tan t + 5 sec t. (b) (5 points) find the interval of existence. The solution is unde ned for all t where cos t = 0. Because the initial condition is de ned at t = 0 the interval of existence is (cid:0) . 2(cid:1): (15 points) solve the initial value problem y = sin x. It is a separable equation. dy dx sin x. 2y dy = sin x dx, r eydy = r 2x dx, R 2y dy = r sin x dx, y2 = cos x + c.
