Matrix A:
1 1
4 1

x' = Ax

( x' = Derivative of x )

Solve for the general solution to the system.

Above is the equation. I'm 90% sure it's linear algebra and supposedly a rather simple equation, however I've no idea how to do it as I've not taken linear algebra yet. Bit desperate for an answer to it, any help would be greatly appreciated!

2. Originally Posted by t16
Matrix A:
1 1
4 1

x' = Ax

( x' = Derivative of x )

Solve for the general solution to the system.

Above is the equation. I'm 90% sure it's linear algebra and supposedly a rather simple equation, however I've no idea how to do it as I've not taken linear algebra yet. Bit desperate for an answer to it, any help would be greatly appreciated!
Let:

$\displaystyle x={x_1 \brack n_2}$,

then we have a pair of coupled ODEs:

$\displaystyle x_1'=x_1+x_2$

$\displaystyle x_2'=4x_1+x_2$

Differentiate the first equation again to get:

$\displaystyle x_1''=x_1'+x_2'=x_1'+4x_1+x_2=2x_1'+3x_1$

which is a homogeneous linear 2nd order ODE which you should be able to solve for $\displaystyle x_1$.

Now do the same to get the 2nd order ODE for $\displaystyle x_2$.

RonL