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### QUESTION 1
The differential equation is:
\[ \frac{d^2i}{dt^2} + 5\frac{di}{dt} + 2i = 3 \sin(2t) \]

Using the method of undetermined coefficients, we find the particular solution for \( i(t) \).

1. **Solve the homogeneous equation:**
\[ \frac{d^2i}{dt^2} + 5\frac{di}{dt} + 2i = 0 \]

The characteristic equation is:
\[ r^2 + 5r + 2 = 0 \]



Learn how to solve a differential equation using the method of undetermined coefficients. This problem involves finding the particular solution for a second-order differential equation with a sinusoidal forcing function. Suitable for advanced undergraduate students studying differential equations.

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