12.10 Exercises 365
x
p(t)
t
Figure 12.9
0 Exercise 39
12.10 Exercises
Section 12.2
1.Show thate
− 2 xande
2 x 23are particular solutions of the differential equation 3 y′′ 1 + 14 y′ 1 − 14 y 1 = 10.
2.Show thate
3 xandxe
3 xare particular solutions of the differential equationy′′ 1 − 16 y′ 1 + 19 y 1 = 10.
3.Show thatcos 12 xandsin 12 xare particular solutions of the differential equationy′′ 1 + 14 y 1 = 10.
Write down the general solution of the differential equation in
4.Exercise 1. 5.Exercise 2. 6.Exercise 3.
Section 12.3
Find the general solutions of the differential equations:
7.y′′ 1 − 1 y′ 1 − 16 y 1 = 10 8. 2 y′′ 1 − 18 y′ 1 + 13 y 1 = 10 9.y′′ 1 − 18 y′ 1 + 116 y 1 = 10
- 4 y′′ 1 + 112 y 1 + 19 y 1 = 10 11.y′′ 1 + 14 y′ 1 + 15 y 1 = 10 12.y′′ 1 + 13 y′ 1 + 15 y 1 = 10
Section 12.4
Solve the initial value problems:
Solve the boundary value problems:
dy
dx
dy
dx
yy y
2
2
++=; =, =8160 0 1() ()01
dy
dx
yy xy x
2
2
+=; =90 0when = =0 1, when =π 2
dy
dx
dy
dx
yy y
2
2
++=; 480 () ( )ππ 24 =−,13 1=
dx
dt
dx
dt
xx
dx
dt
2
2
−+=; =, 2200100 () ()=
dx
dt
xx
dx
dt
2
2
+=;90 30 3 1()ππ=, ()=−
dx
dt
dx
dt
xx
dx
dt
2
2
++=; =,69010 11() ()=
dx
dt
dx
dt
xx
dx
dt
2
2
+−=;20 01 00()=, ()=