## Brandie 3 years ago write in matrix form: x'=y, y'=x+4 my teacher has not gone over this, I need help

1. amistre64

what is matrix form?

2. amistre64

some sort of subject that this pertains to would help out as well

3. Brandie

I am working with differential equations

4. amistre64

diffy qs, thats a start :)

5. amistre64

and is this the start of a problem or like midways thru?

6. Brandie

does x'=Ax+b help?

7. Brandie

sorry, full question: write each system of differential equations in matrix form, i.e. x'=Ax+b

8. amistre64

let me look that up to see if im familiar with it by another name ...

9. amistre64

this looks useful http://tutorial.math.lamar.edu/Classes/DE/SystemsDE.aspx

10. Brandie

yeah, its actually helping me on other questions, but not this one. But thanks. :)

11. amistre64

is your vector [x',y'] by chance?

12. Brandie

idk, a vector was not mentioned

13. amistre64

x'=0x+y+0 y'=x+0y+4 $\binom{x'}{y'}=\begin{pmatrix}0&1&0\\1&0&4 \end{pmatrix}\binom{x}{y}$ maybe

14. amistre64

matrixes are vectors ...

15. amistre64

$\binom{x'}{y'}=\begin{pmatrix}0&1\\1&0 \end{pmatrix}\binom{x}{y}+\binom{0}{4}$ maybe

16. Mr.Math

We have the system $$x'=0x+y$$ $$y'=x+0y+4$$. We can write this as: $${x' \choose y'}=\left[\begin{matrix}0 & 1 \\ 1 & 0\end{matrix}\right]{x\choose y}+{0\choose 4}.$$

17. amistre64

yay!! thats good enough for validation to me :)

18. Brandie

really? i thought it was more involved than that, cool. Thanks guys!

19. Mr.Math

Although I think it can be solved without finding any eigenvalues or eigenvectors.