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## NAU Limits General Solutions Arbitrary Constants & Discriminant Worksheet

### Question Description

1. Find the general solution for each of the following differential equations. Additionally, calculate lim y for solutions of the differential equation.

t??

Please indicate all possibilities for this limit and if/how they depend on the constants c1 and c2.

a) 4y?? + 16y? + 17y = 0

b) y?? ? 4y? + 4y = 0

2. Describe all possibilities for solutions of the following differential equation in terms of the parameter k. That is, you should determine values of k that will lead to the three distinct types of roots we have discussed and state the corresponding general solutions.

y?? + ky? + 4y = 0

3. Solve the following initial value problem.

y?? ?5y? ?14y=?14t+37 withy(0)=?3andy?(0)=?6

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