First-Order Differential Equations – Euler Method | Lecture 2″,”navigationEndpoint”:{“clickTrackingParams”:”CJgDEJHeChgVIhMI7Yv-pPiugAMVwEj1BR1KpgQD”,”loggingUrls”:[{“baseUrl”:”https://www.youtube.com/pagead/paralleladinteraction?ai=CxlLx6mnCZOKcBPG-vcAP3eaC8AUAxbTp1cERABABIABgwQWCARNwYXJ0bmVyLXlvdXR1YmUtc3JwqAMEqgQXT9DFtau7dg05Hs1p2eT6Y0deK6wTqWyQBwSoB-edsQKoB-idsQKoB4QIqAfOp7EC0ggRCIBBEAEYXjICggI6AoBAUBSwCwG6Cz4IAxAFGAwgCygFMAVAAUgAWGpgAGgAcAGIAQCQAQGYAQGiAQsKAJgCAqgCAdgCAqgBAcABAdABAeABAYACAaAXAQ\u0026sigh=05PsE1Jm1us\u0026cid=CAASFeRoeo5T8B9TOcHDKecmpQXRD8rLpA\u0026ad_mt=[AD_MT]\u0026acvw=[VIEWABILITY]\u0026gv=[GOOGLE_VIEWABILITY]\u0026nb=%5BNB%5D\u0026label=video_click_to_advertiser_site
First-Order Differential Equations – Euler Method | Lecture 2″,”navigationEndpoint”:{“clickTrackingParams”:”CJgDEJHeChgVIhMI7Yv-pPiugAMVwEj1BR1KpgQD”,”loggingUrls”:[{“baseUrl”:”https://www.youtube.com/pagead/paralleladinteraction?ai=CxlLx6mnCZOKcBPG-vcAP3eaC8AUAxbTp1cERABABIABgwQWCARNwYXJ0bmVyLXlvdXR1YmUtc3JwqAMEqgQXT9DFtau7dg05Hs1p2eT6Y0deK6wTqWyQBwSoB-edsQKoB-idsQKoB4QIqAfOp7EC0ggRCIBBEAEYXjICggI6AoBAUBSwCwG6Cz4IAxAFGAwgCygFMAVAAUgAWGpgAGgAcAGIAQCQAQGYAQGiAQsKAJgCAqgCAdgCAqgBAcABAdABAeABAYACAaAXAQ\u0026sigh=05PsE1Jm1us\u0026cid=CAASFeRoeo5T8B9TOcHDKecmpQXRD8rLpA\u0026ad_mt=[AD_MT]\u0026acvw=[VIEWABILITY]\u0026gv=[GOOGLE_VIEWABILITY]\u0026nb=%5BNB%5D\u0026label=video_click_to_advertiser_site

So, I am trying to attempt part b of this problem using my answer from part a. I just want to confirm if I did part a correctly and how I can do part b?

How can I use Euler’s Method in order to find the value of a constant k given the differential equation?

  • $\begingroup$ Related : How do I find the values of the constants for which $y = ax + b +e^{cx}$ is a solution to the differential equation given. A solution was already provided for part (a). What ideas do you have about part (b)? You need to show some effort. See eg Euler’s method approximating differential equations $\endgroup$ Mar 29, 2020 at 19:02
  • $\begingroup$ I pretty sure I actually can do part b, but I’m skeptical of part a. I’m not sure if it is right. $\endgroup$ Mar 29, 2020 at 19:05
  • $\begingroup$ However, I will try to see what I can come up with in part b. $\endgroup$ Mar 29, 2020 at 19:06
  • $\begingroup$ ok, so I tried the Euler method and solved for k and I got k = -7/9. Is there a way I can check to make sure this is correct? $\endgroup$ Mar 29, 2020 at 19:21

1 Answer

hint

There are two possibilities :

with Euler after, $\; $ at $ x=0 $, the equation is $$f'(0)=\frac{f(1)-f(0)}{\Delta x}=2f(0)+1$$

thus $ k=-\frac 13.$

Euler before, $\; $ at $ x=1 $, gives

$$f'(1)=\frac{f(1)-f(0)}{\Delta x}=3+2f(1)+1$$ hence $ k=- 4$.

  • $\begingroup$ So I tried to do the Euler Method and I got k = -7/9. However, I am not sure if this is correct. Is there a way for me to check my solution? $\endgroup$ Mar 29, 2020 at 19:25
  • $\begingroup$ I plugged in -7/9 in the Euler Method and I got f(1) = 0. So I think I have my solution $\endgroup$ Mar 29, 2020 at 19:28

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