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

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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