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

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

... Solution:- Comparing the equation. ... The Partial Differential Equation (1) is hyperbolic when the ... Hence the given partial difference equation is hyperbolic ...

Step by Step Explanation of Differential Equations. ... Please find the general solution of: (1) dy/dx = y/sin(y) - x (2) dy ... Explain similarities and differences. ...

... This well-presented solution shows how to solve differential equations related to free fall ... The difference between these two models is in the transient status ...

... Problem 1 Given = +2 +3 a) Find the difference quotient +ℎ − ℎ b) Use the definitional formula given below ... at x = 3. Word-process your solution below ...

... 5) form a system of linear differential equations of 1 ... following boundary conditions: ( 6) The solution of the ... there will be no significant differences on the ...

... This solution is provided in 454 words in an ... It is a linear, nonhomogenous differential equation with non ... as it is represented by a linear difference equation. ...

... Now we find k2 using the following equation. ... Runge-Kutta From actual solution t Difference Value of y(t) Value of y(t) 0.5 1.214041 1.214023 0.000018. ...

... means that the analysis is the same, the only difference is the ... 1.64) We distinguish between three cases: Case 1: The equation is and its solution is (1.65 ...