1. Exam DE

Hello! This is my first post in this forum, I spend mamy time in this exercise, but I can't iron out. Maybe someone help me? It's very important for me, because in september I need pass the exam.
$x^{,}_{1}=(a+1)x_{1}-ax_{2}\\x^{,}_{2}=(3a-1)x_{2}+ax_{1}$
$x_{1}(0)=1,x_{2}(0)=a$
Find:
$\frac{\partial x}{\partial a}\ for\ a=0\ where\ x=(x_{1},x_{2})$

2. Re: Exam DE

I presume that if you are taking an exam in September, then you are taking the course now. Certainly, you must have learned something about problems like this. How would you solve a system of equations like this?

3. Re: Exam DE

I think this is not tall order, I can solve this equation : dx/dt= ax-t-a; x(0)=1, Find dx/da(t) for a=0, but this I can't find the correct answer.

4. Re: Exam DE

Then you should not be attempting an equation like this. There are several different ways, involving reducing to a single second order equation or finding eigenvalues of a related matrix, but you seem to be saying you do not know those. Learn higher order linear differential equations before attempting systems of equations.