Reference no: EM13912693
1. First-order differential equations
Solve the following and study the behavior of x(t) when t → ∞.
a. 2x'(t)+8x(t) = 6, with x(0) = 10
b. x'(t)+5x(t)/t = t, with x(1) = 1
c. x'(t)+ x(t) = t, with x(1) = 10
d. x'(t)+ t x(t) = t, with x(0) = 1
2. First-order difference equations
Solve the following and study the behavior of xt when t → ∞.
a. 4xt+1 -2xt = 4, with x0 = 2
b. 4xt+1 +2xt = 4, with x0 = 2
c. 2xt+1 -2xt = 7, with x0 = 0
d 2xt+1 +2xt = 3, with x0 = 0
3. Second-order differential and difference equations
Solve the following and study the behavior of xt when t → ∞.
a. 2x''(t)+8x(t) = 0, with x(0) = 1 and x'(0) = 0
b. x''(t)+5x'(t)+6x(t) = 1, with x(0) = 1 and x'(0) = 0
c. x''(t)+2x'(t)+ x(t) = 1, with x(0) = 1 and x'(0) = 1
d. xt+2 +4xt+1 +3xt = 10, with x0 = 0 and x1 = 5
e. xt+2 +4xt+1 +4xt = 10, with x0 = 0 and x1 = 5
4. Systems of differential and difference equations
Solve the following systems:
5. Diagrammatic analysis
Consider the system of equations 4 a.
a. Perform a diagrammatic analysis.
b. Will the system converge?
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