Inhomogeneous system of DE in matrix form \dot x = 2x

Wertgenib6

Wertgenib6

Answered question

2022-04-23

Inhomogeneous system of DE in matrix form
x˙=2x+y+3et
y˙=4xy

Answer & Explanation

Litzy Fuentes

Litzy Fuentes

Beginner2022-04-24Added 22 answers

Step 1
We can write this as the system
X(t)=AX(t)+g(t)=
(2141)(xy)+(3et0)
You could then solve the homogeneous and non-homogeneous part using many different approaches.
If you are looking for theory and examples, see these notes or notes or notes.
If you solve these, you would get
x(t)=15c1e2t+45c1e3t15c2e2t+15c2e3tet
y(t)=45c1e2t+45c1e3t+45c2e2t+15c2e3t2et

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?