1. Find a Particular Solution using undetermined coefficients, then find a general solution y³ + y" - 6y' = 3e²ⁿ.
2. Find a particular solution using the method of variation of parameters then find a general solution y" + 9y = cos(3x).
3. Solve the Initial Value Problem x" + 4x = 6sin(3t). x(0)=4, x'(0) = 0.
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Differential equations are solved by findin general and particular solutions. An initial-value problem is also solved. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.