Math 285 Mid Term 1 Practice Sp, 2017 Manfroi
1. Replace the second order differential
equation with two first order y’’
= (dy/dt) sin y = 0 Answer: dw/dt = w sin y, dy/dt = w |
2. Find the Wronskian
of the two functions: y1(t) = exp(3t2
+ 8) and y2(t) = exp(3t2 ˗
4) Answer: Wr = 0 |
3. The existence and uniqueness theorem for
linear differential equations ensures that the solution of (t ˗
2)(t+ 3) y'' + t(t˗2)y' + t2 y =
(1/(t+5), y(˗6) = 2, y'(˗6)
= 5 exists for what region? Answer: (˗∞, ˗5) U (˗5,
˗3) U (˗3,2) U (2,∞) |
4. Transform the following differential
equation into a separable differential equation. dy/dt = (t + 4y) /
(5t ˗ y) Answer: dv / (v2
˗ v +1) = dt/t where
v = y/t |
5. Transform the differential y' + (sint)
y =
(cos t) y5 into a linear, first order differential equation. Answer: dv/dt ˗ (4 sin t) v
= ˗ 4 cos
t where v = y˗4 |
6. Find the order of the following
differential equation: (y')5 +
3(y')4 + 2(y')3 ˗ (y')2 + 10
y' =
0 Answer: 1 |
7. Given a slope field. Identify the corresponding differential
equation. Click here to continue with
this practice exam. |