Lecture 4.9: Variation of parameters for systems

Lecture 4.9: Variation of parameters for systems

Matthew Macauley

Department of Mathematical Sciences

Clemson University



Math 2080, Differential Equations

M. Macauley (Clemson)

Lecture 4.9: Variation of parameters for systems

Differential Equations

1/6

Variation of parameters for non-systems

Variation of parameters is a ¡°last resort¡± method for finding a particular solution, yp (t).

First order ODE: y 0 + p(t)y = f (t)

M. Macauley (Clemson)

Lecture 4.9: Variation of parameters for systems

Differential Equations

2/6

Variation of parameters for non-systems

Variation of parameters is a ¡°last resort¡± method for finding a particular solution, yp (t).

First order ODE: y 0 + p(t)y = f (t)

(i) Solve yh0 + p(t)yh = 0:

M. Macauley (Clemson)

Lecture 4.9: Variation of parameters for systems

Differential Equations

2/6

Variation of parameters for non-systems

Variation of parameters is a ¡°last resort¡± method for finding a particular solution, yp (t).

First order ODE: y 0 + p(t)y = f (t)

(i) Solve yh0 + p(t)yh = 0: get yh (t) = Cy1 (t)

M. Macauley (Clemson)

Lecture 4.9: Variation of parameters for systems

Differential Equations

2/6

Variation of parameters for non-systems

Variation of parameters is a ¡°last resort¡± method for finding a particular solution, yp (t).

First order ODE: y 0 + p(t)y = f (t)

(i) Solve yh0 + p(t)yh = 0: get yh (t) = Cy1 (t) = Ce ?

M. Macauley (Clemson)

R

p(t) dt .

Lecture 4.9: Variation of parameters for systems

Differential Equations

2/6

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