Matrix presentation of ode \left ( \begin{matrix}x'_1 \\x'_2

Erika Bernard

Erika Bernard

Answered question

2022-04-16

Matrix presentation of ode
(x1'x2')=(4113)x1x2
Is it possible to write this ode in one equation ? write if it is possible.
How am I supposed to know this ?

Answer & Explanation

Juan Goodwin

Juan Goodwin

Beginner2022-04-17Added 10 answers

Step 1
This process is called decoupling the equations. We have two DEs
x1'=4x1+x2x2'=x1+3x2.
Differentiating the first equation once, we obtain x1 =4x1+x2.
Step 2
Substituting x2  using the second equation, we get
x1 =4x1+x1+3x2.
We still need to replace x2, which can be done using the first equation again x2=x1 4x1. Hence,
x1 =4x1+x1+3(x14x1)
or x1 7x1+11x1=0.

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