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Solving Difference Equation and Differential Equation

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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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https://brainmass.com/math/complex-analysis/solving-difference-equation-and-differential-equation-583642

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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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Differential and difference equation

Please help with the following problem, providing step by step calculations in the solution.

Solve the differential equation subject to y(0)=2. An Euler approximation to y(x)=2. An Euler approximation to y(x) is given by setting h=x/h, solving the difference equation:

See attached file for equations and full problems.

With initial condition y0=2. The approximation is then y(x)=yn, and show that if n is large, this approximates y(x).

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