Nonhomogeneous systems

Forcing added to a system: integrating-factor and eigenvector-decomposition approaches, variation of parameters, and undetermined coefficients for simple drives.

Notes on Diffy Qs: Differential Equations for Engineers, Nonhomogeneous systems

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4 exercises

Exercise 101

Find a particular solution to $x' = 5x + 4y + t$ , $y' = x + 8y - t$

using integrating factor method,
using eigenvector decomposition,
using undetermined coefficients.

2.5

Exercise 102

Find a particular solution to $x' = y + e^t$ , $y' = x +e^t$

using integrating factor method,
using eigenvector decomposition,
using undetermined coefficients.

2.5

Exercise 103

Solve $x_1' = x_2 + t$ , $x_2' = x_1 +t$ with initial conditions $x_1(0) = 1$ , $x_2(0) = 2$ using eigenvector decomposition.

2.5

Exercise 104

Solve $x_1'' = -3x_1 + x_2 + t$ , $x_2'' = 9x_1 + 5x_2 +\cos(t)$ with initial conditions $x_1(0) = 0$ , $x_2(0) = 0$ , $x_1'(0) = 0$ , $x_2'(0) = 0$ using eigenvector decomposition.

2.5