More review problems
MATH 1220, Spring 2005
(1)
(2)
(3)
(4)
(5)
(§18.1)
(§18.1)
(§18.2)
(§18.2)
(§18.2)
Solve the differential equation:
Solve the differential equation:
Solve the differential equation:
Solve the differential equation:
Using the Method of Variation
y ′′ + 2y ′ − 8y = 0.
(D3 − 4D2 + 6D)y = 0.
y ′′ + 3y ′ − 4y = 4x2 − 6x − 10.
y ′′ − 4y = cos 2x − sin 2x.
of Parameters solve the following differential equation:
y ′′ − 3y ′ + 2y = 5x + 2.
(6) (§18.3) A 12 pound weight stretches a spring 2 inches. The weight is raised 2 inches and given an initial
velocity of 2 feet per second upward. Find the equation of the motion.
(7) (§18.3) A spring with constant k of 10 pounds per foot is loaded with a 32 pound weight and brought to
equilibrium. It is the stretched 2 inches and released. Find the equation of the motion if the damping force is
proportional to twice the velocity.
1
2
Answers to more review problems
MATH 1220, Spring 2005
(1) y = C1 e2x + C2 e−4x .
√
√
(2) y = C1 + e2x (C2 sin 2x + C3 cos 2x).
(3) y = C1 e−4x + C2 ex + 2 − x2 .
1
(4) y = C1 cos 2x + C2 sin 2x + x(cos 2x + sin 2x).
4
19
5
(5) y = C1 e2x + C2 ex + x + .
4
√2
√
√
1
3
sin 8 3t.
(6) y = − cos 8 3t −
6
12
1
1
−t
cos 3t +
sin 3t .
(7) y = e
6
18