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As we now we can use StreamPlot to visualize first-order differential equations like:y'[x]==1+x-y

StreamPlot[{1, 1 + x - y}, {x, -3, 3}, {y, -3, 3}, Axes -> True, 
 Frame -> False]

enter image description here

But how about second-order differential equations? Such as y''[x]+2y'[x]+3y==0?Can we visualize it?

yode
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  • Please see the above link. It shows how to do it for second order ODE. – Nasser Oct 20 '21 at 08:16
  • @Nasser It's hard to imagine this topic with such a title. I searched for a long time and didn't find it. – yode Oct 20 '21 at 08:18
  • I agree on the title, but I just remembered it myself and searched for it. – Nasser Oct 20 '21 at 08:20
  • @Nasser Are you saying you have memorized the title you quoted? – yode Oct 20 '21 at 08:23
  • No, I meant I remembered similar question was asked before, so was able to find it by googling. I have good memory :) – Nasser Oct 20 '21 at 08:25
  • If we make y'=x, then we can convert it into {y',x'}={{1,0},{-2,-3}}.{x,y}, then we can use StreamPlot – yode Jan 09 '24 at 06:38

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