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Solving Difference Equation and Differential Equation

1. Complex Exponentials: Simply the following expression and give your answer both in polar and rectangular form.

o c=3ejπ/4+4e−jπ/2
2. Difference Equations: Solve the following difference equation using recursion by hand (for n=0 to n=4)
o y[n] + 0.5y[n-1] = 2x[n-1]; x[n] = δ[n], y[-1] = 0
3. Differential Equations: Solve the following problem for y(t).
o dy/dt + 2y(t) = 2x(t); x(t) = u(t), y(0) = −1

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The solution gives detailed steps on solving difference equation, solving differential equation and simplifying complex exponential in polar and rectangular form.

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