Homework # 6 - Math 328
The problems on this homework must be done alone. The honor code is in effect.
First name: Last name:
1. Consider the initial value problem \(y'' - y' - 2y = 0\), such that \(y(0) = 1\), \(y'(0) = 0\). Then, as \(x\rightarrow\infty\),
b. \(y \rightarrow 0\)
b. \(y \rightarrow +\infty\)
c. \(y \rightarrow -\infty\)
d. \(y \rightarrow 2\)
e. The limit of y doesn't exist.
2. Consider the initial value problem \(y'' - y' - 2y = 0\), such that \(y(0) = 1\), \(y'(0) = -1\). Then, as \(x\rightarrow\infty\)
3. Write out and submit your solution for questions 1 and 2.
4. If \(y_1(t) = t\) is a solution to \(t^2y''+2ty'-2y = 0\), find a second solution \(y_2(t)\) that is not a multiple of \(y_1(t)\) by using the method of reduction of order.
5. Solve the following differential equations.
a) \(y'' - 6y' + 8y = 0\)
b) \(y'' - 6y' + 9y = 0\)
c) \(y'' - 6y' +10y = 0\)