Solve linear system of ODE's It's been years since I formally saw ODE's and I am quite rusty, I

Esther Hoffman

Esther Hoffman

Answered question

2022-04-22

Solve linear system of ODE's
It's been years since I formally saw ODE's and I am quite rusty, I don;t remember how to solve linear ODE's.
I have a problem and managed to derive the following system:
{2q1¨=2q1+q22q2¨=q1
where q1 and q2 are scalar functions with parameter t.
It seems to me the solution is a trig function but I am not sure how to go about this problem.

Answer & Explanation

obettyQuokeperg6

obettyQuokeperg6

Beginner2022-04-23Added 14 answers

Step 1
q2=2q12q1. Then q2=2q12q1. So,
4q14q1=q1 or 4q14q1q1=0.
The characteristic equation is 4r44r21=0 and has four different real solutions.
Step 2
r1,2=±122 and r3,4=±1+22
q2=Aer1t+Ber2t+Cer3t+Der4t
From here you can derive q1.

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