Download MATH 308 Homework 4

Texas A&M University
Department of Mathematics
Volodymyr Nekrashevych
Spring 2013
MATH 308 Homework 4
4.1. Find the general solution of the differential equation
y 00 − 2y 0 − 3y = −3te−t .
4.2. Find the solution of the initial value problem
y 00 + 4y = 3 sin 2t,
y(0) = 2, y 0 (0) = −1.
4.3. Use the method of variation of parameters to find the general solution
of the differential equation
y 00 + 4y 0 + 4y = t−1 e−2t ,
t > 0.
4.4. Verify that the given functions y1 and y2 satisfy the corresponding
homogeneous equation; then find a particular solution of the given
nonhomogeneous equation.
t2 y 00 − 2y = 3t2 − 1,
t > 0;
y1 (t) = t2 ,
y2 (t) = t−1 .
4.5. A mass of 5 kg stretches a spring 10 cm. The mass is acted on by
an external force of 10 sin(t/2) newtons and moves in a medium that
imparts a viscous force of 2 newtons when the speed of the mass is 4
cm/s. If the mass is set in motion from its equilibrium position with
an initial velocity of 3 cm/s (downward), formulate the initial value
problem describing the motion of the mass.
4.6. Find the Laplace transform of teat using integration by parts.