
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the general solution \( y=C_{1} \sin 2x + C_{2} \cos 2x \) of the differential equation \( y^{\prime \prime} + 4y = 0 \):

1. What particular solutions are obtained for \( C_{1} = 2 \) and \( C_{2} = 3 \)?
2. For which values of the parameters \( C_{1} \) and \( C_{2} \) are the particular solutions \( y = \sin 2x \) and \( y = \cos 2x \) obtained?

Present the answer in LaTex format: \boxed{Your answer}
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