Not sure what the problem is asking (21 exercises)

[zolteckx6]

So after I find the equilibrium points I separate and solve the DE plug in the Initial condition and plot the solution? is that right? DE has been really hard for me and I'm not sure why. I went through calc 3 just fine but DE and parameters have been a real struggle. At any rate is what I stated in bold the correct way to solve these exercises? I thank you for anyone's time and patience with me.

 

[tkhunny]

View attachment 9749

So after I find the equilibrium points I separate and solve the DE plug in the Initial condition and plot the solution? is that right? DE has been really hard for me andView attachment 9749 I'm not sure why. I went through calc 3 just fine but DE and parameters have been a real struggle. At any rate is what I stated in bold the correct way to solve these exercises? I thank you for anyone's time and patience with me.

It might help if you shared and actual example. 1-9 seem to be missing. Anyway, it looks like you arenot too far...

1) Solve the Differential Equation with an arbitrary parameter.
2) Substitute the given condition to create a specific solution.
3) Draw the graph of that specific solution.

 

[zolteckx6]

It might help if you shared and actual example. 1-9 seem to be missing. Anyway, it looks like you arenot too far...

1) Solve the Differential Equation with an arbitrary parameter.
2) Substitute the given condition to create a specific solution.
3) Draw the graph of that specific solution.

yeah, so I think you are right too. Thank you for clearing that up for me just for the record my confusion was if I actually had to solve the equation because if I just SKETCH as it says in the exercises and the fact that I'm on equilibria and the phase line and the actual examples that are missing (ill post them) ask me to sketch the phase lines for the given differential equation. I can kinda generalize what the solutions look like and I'm doing this without instructor so lol idk maybe it's "however I feel like doing it at this point" although I don't care for that attitude.

 

[zolteckx6]

It might help if you shared and actual example. 1-9 seem to be missing. Anyway, it looks like you arenot too far...

1) Solve the Differential Equation with an arbitrary parameter.
2) Substitute the given condition to create a specific solution.
3) Draw the graph of that specific solution.

 

[HallsofIvy]

So problem 13 is asking you to solve the differential equation \(\displaystyle \frac{dy}{dt}= 3y(y- 2)\) four times, the first time, subject to the requirement that y(0)= 1, the second time with y(-2)= -1, the third time with y(0)= 3, and the fourth time with y(0)= 2. Did you do problem 1? That is, did you find the general solution to \(\displaystyle \frac{dy}{dt}= 2y(y- 2)\) which involves one undetermined constant? If you have then you just have to determine that constant so that the additional condition is satisfied.

 

[Dr.Peterson]

So problem 13 is asking you to solve the differential equation \(\displaystyle \frac{dy}{dt}= 3y(y- 2)\) four times, the first time, subject to the requirement that y(0)= 1, the second time with y(-2)= -1, the third time with y(0)= 3, and the fourth time with y(0)= 2. Did you do problem 1? That is, did you find the general solution to \(\displaystyle \frac{dy}{dt}= 2y(y- 2)\) which involves one undetermined constant? If you have then you just have to determine that constant so that the additional condition is satisfied.

As I read it, none of this asks you to actually solve a differential equation. It's all about sketching graphs.

Problem 1 says "Sketch the phase lines and identify the equilibrium points". Here is one source for this concept; here is another.

Problem 13 says "Sketch the graphs of the solutions". The same references show how to do this.

Presumably the OP has been taught this, but seems to think solving is necessary. It isn't (though, of course, it could be done). I would hope there were some examples.

If problem 1 had been included in the original submission, this would have been understood from the start, and less confusion would have arisen.

 

[zolteckx6]

As I read it, none of this asks you to actually solve a differential equation. It's all about sketching graphs.

Problem 1 says "Sketch the phase lines and identify the equilibrium points". Here is one source for this concept; here is another.

Problem 13 says "Sketch the graphs of the solutions". The same references show how to do this.

Presumably the OP has been taught this, but seems to think solving is necessary. It isn't (though, of course, it could be done). I would hope there were some examples.

If problem 1 had been included in the original submission, this would have been understood from the start, and less confusion would have arisen.

I am sorry for the lack of Information I gave. I won't let it happen again. I did not think I needed to solve the eq as you say "Sketch the graphs of the solutions". I was a bit confused though and now I'm not thank you for clearing this up.

 

[Dr.Peterson]

I am sorry for the lack of Information I gave. I won't let it happen again. I did not think I needed to solve the eq as you say "Sketch the graphs of the solutions". I was a bit confused though and now I'm not thank you for clearing this up.

Actually, I was commenting mostly for the sake of others, as I figured in the month and a half since the question, you would have moved beyond this. It's unfortunate that the moderation process causes responses to be posted late but under the time they were submitted, which may by then be far down the list of posts, so that too often they are missed; if I'd seen this one I probably would have made sure to respond to it.

I'm glad you did figure it out.

 

[HallsofIvy]

Okay, to "sketch the solutions" without actually solving, use the differential equation to draw some tangent lines. In problem 13, the differential equation is dy/dx= 3y(y-2). That derivative is the slope of the tangent line at each (x, y) point. This is easy here since that depends only on y. When y= 0 or 2, dy/dx= 0 so just draw a horizontal line at each of those. At, say, y= 1, dy/dx= 3(1)(1-2)= -3 so draw a whole series of short lines, centered at (x, 1) for different x with slope -3. etc.

 

[elensimons]

It's always easy to get confused with the differential equations. thanks for bringing this up as it was really helpful for me to see the comments.