# Math-StudyGuideforExam3.docx

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1. Find the general solutions of the given differential equations, initial value problem, and system using whichever method that seems appropriate.

a) 𝑦(“) − 12𝑦\$\$\$ + 53𝑦\$\$ − 100𝑦\$ + 68𝑦 = 500𝑒%&

b) 𝑥’𝑦\$\$\$ − 7𝑥%𝑦\$\$ + 24𝑥𝑦\$ − 34𝑦 = 50𝑥%, 𝑥 > 0

c) 8𝑦\$\$\$ − 12𝑦\$\$ + 6𝑦\$ − 𝑦 = 960𝑒&⁄%

d) 𝑥%𝑦\$\$ = 𝑦′(3𝑥 − 2𝑦\$)

e) 4𝑦(𝑦\$)%𝑦\$\$ = (𝑦\$)” + 3, assume x is the independent variable.

f) 2𝑥\$ + 2𝑥 + 𝑦\$ − 𝑦 = 𝑡 + 1,𝑥\$ + 3𝑥 + 𝑦\$ + 𝑦 = 4𝑡 + 14. (Eliminate x first!)

2. Find the first six non-zero terms of a Taylor series solution to the initial value problem:

2𝑦’ − 4𝑒)&𝑦\$ − 𝑦\$\$ = 𝑥% sin 𝑥 ,𝑦(0) = −3,𝑦\$(0) = 1

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