Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have these functions:

$x' (t) = −5x(t) + 2 y(t)$

$y' (t) = 2x(t) − 2y(t)$

where $x(0)=10$ and $y(0)=0$

I am also given these 2 functions:

$z(t) = x(t) + 2y(t)$

$w(t) = −2x(t) + y(t)$

First question is to express $z'(t)$ and $w'(t)$ in terms of $x'(t)$ and $y'(t)$


$z'(t) = x'(t) + 2y'(t)$

$w'(t) = -2x'(t) + y'(t)$

Easy enough. I am then asked to express $z'(t)$ and $w'(t)$ in terms of $z(t)$ and $w(t)$, but I don't know how to do that!

Can I get some pointers? Thanks!

share|cite|improve this question
For example $z'=x'+2y'=(-5x+2y)+2(2x-2y)=-x-2y=-(x+2y)=-z.$ – Git Gud Jun 15 '14 at 19:46
ugh that makes sense. I am so bad. Thanks ! – Kevin Jun 15 '14 at 20:11
You're welcome. If no one posts an answer, I suggest you answer the question yourself, so it doesn't come up as unanswered. – Git Gud Jun 15 '14 at 20:13

$$\textbf{Note: this is just tidying up question with an answer as provided by @GitGud.}\\ \textbf{So please refrain from voting on this question.}$$

$$ z' = x' + 2y' = (-5x+2y) + 2(2x-2y) = -x -2y = -(x+2y) = -z $$

Similarly for $w$ we find:

$$ w' = -2(-5x+2y) + (2x-2y) = 12x -6y = 6(2x - y) = -6w $$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.