MATH 316 F09 Quiz 2 Solutions
1. Use the Laplace transform to solve the following initial-value problem:
y 6y + 9y = t, y(0) = 0, y (0) = 1.
Solution Let Y = Lcfw_y. Then Lcfw_y = sY and Lcfw_y = s2 Y 1. Taking the Laplace
transform of the dierential
MATH 316 F09 Quiz 1 Solutions
1. Find the general solution to the dierential equation y + x y + (1 x2 )y = 0. Express
your answer in terms of power series.
Solution Multiplying the equation by x2 we obtain x2 y + xy + (x2 4)y = 0. This is
MATH 316 F09 Quiz 4 Solutions
1. Solve the following boundary-value problem for the wave equation
, 0 < x < L, t > 0
u(0, t) = 0, u(L, t) = 0
u(x, 0) =
Solution Let u(x, t) = X(x)T (t). Then we have a2 X T =
MATH 316 F09 Test 1 Solutions
1. Verify that x = 0 is ordinary point of the dierential equation (1 + x)y + y = 0. Then
nd two linear independent power series solutions. For each solution, nd the rst four
terms of the series.
Solution In standard for
Review Problems for Final Exam
Regular Singular Points and Method of Frobenius
1. Determine whether x = 0 is a regular singular point of the differential equation x y
+ 2x2 y + y =
2. Find the general solution near x
= 0 of 8x2 y + 10
Review Problems for Test 2
System of Equations
1. Solve the system
+ 8 + C1 ,
+ y = 0,
+ 2x + 2
2y = t .
8 + C1 .
2. Solve each of the following systems using Laplace transforms:
y = t , x