# Exam DE

• Aug 27th 2012, 08:17 AM
anka0501
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.
$\displaystyle x^{,}_{1}=(a+1)x_{1}-ax_{2}\\x^{,}_{2}=(3a-1)x_{2}+ax_{1}$
$\displaystyle x_{1}(0)=1,x_{2}(0)=a$
Find:
$\displaystyle \frac{\partial x}{\partial a}\ for\ a=0\ where\ x=(x_{1},x_{2})$
• Aug 27th 2012, 09:39 AM
HallsofIvy
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?
• Aug 28th 2012, 01:00 AM
anka0501
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.
• Sep 8th 2012, 06:52 AM
HallsofIvy
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.