Mat 275 Modern Differential Equations
Mat 275 Modern Differential Equations Lecture week 5
Final Exam Review Section 1.1-7.2 (Second Summer 2006)
Department of Mathematics and Statistics
Arizona State University
1. Show that [pic] [pic] are the solutions of [pic]. Find the general solution.
2. Find general solution of the following functions:
a) [pic] b) [pic]
c) [pic] d) [pic]
e) [pic] f) [pic]
g) [pic] h) [pic]
i) [pic] j) [pic]
k) [pic] l) [pic]
3. Solve the initial value problems:
a) [pic] b) [pic]
c) [pic] d) [pic]
4. Given that [pic], show that [pic] and [pic]
5. The line tangent to the graph of [pic] at [pic] intersects the x-axis at [pic]. Write a differential equation of the form [pic].
6. Solve following system of differential equations by eigenvalue method:
[pic]
7. Show that [pic]are linearly independent. Use Wronskian.
8. a) Find Laplace transform of the following functions:
[pic]
b) Sole the differential equation [pic]by Laplace Transform and inverse Laplace Transform.
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