1. ## Coupled differential equations

Anyone know how to solve these equations without using eigenvalues/eigenvectors?
Can these be solved using standard integration techniques?

dx/dt = 4x+2y
dy/dt = -x +y where x and y are functions of t.

2. ## Re: Coupled differential equations

$\frac{d^{\, 2}x}{dt^{2}}=4\frac{dx}{dt}+2\frac{dy}{dt} = 4\frac{dx}{dt}-2x+2y = 4\frac{dx}{dt}-2x+\left(\frac{dx}{dt}-4x\right)$

so

$\frac{d^{\, 2}x}{dt^{2}} - 5\frac{dx}{dt}+6x = 0,$ etc.

3. ## Re: Coupled differential equations

Many thanks... Seems obvious now!

4. ## Re: Coupled differential equations

You will need to do something similar to get a DE for y as well.

5. ## Re: Coupled differential equations

Still working on this...

I am now trying to understand why the eigenvalues of the matrix of coeff on the RHS are the powers for the solution to the auxilliary equation?
Can anyone help?