# MATH 420 California State University Differential Equation Questions

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Math 420: Assignment 5
Please show all work. Good luck. This assignment is due on Tuesday, October 6 at
5:00 PM.
1) Verify that the given functions form a fundamental set of solutions of the
differential equation on the indicated interval. Form the general solution.
1
x
2
1
x
2
4 yʹʹ − 4 yʹ + y = 0 , e , xe , −∞,∞
(
)
2) The given family of functions is the general solution of the differential
equation on the indicated interval. Find a member of the family that is a
solution of the initial value problem.
y = c1e 4 x + c2e − x , −∞,∞
(
)
yʹʹ − 3 yʹ − 4 y = 0 ; y(0) = 1, yʹ(0) = 2

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differential equation

Applied mathematics

general solution

Value problem

functions form

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