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Completely lost -- just started my O.D.E course this week

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Main Question or Discussion Point

I am completely lost. I just started my O.D.E course this week and I'm already sinking. After the first lecture I was reading through the chapter (because that normally helps) and I became even more confused. I looked at the homework, and I didn't even know where to start. Then I realized (with a glimmer of hope in my eyes) that the professor hadn't even talked about the section that the homework was from. So I was excited about today's lecture because he was going to clear the muddy water... Nope that isn't what happened at all. He mostly talked about the different types of differential equations, said something about a general form, wrote initial value problem on the board and then BOOM!! On to the next chapter. He then realized that he had gone a little over time and apologized.

He didn't explain how to approach the problem, or say if there is a process or goal like move things over here or take a derivative first then integral.

I want to love this class and I'm so excited to be taking it. But I'm already so confused that I spend my time inn a daze asking what just happened to my brain. The material isn't "hard" yet...the hw assigned is for section 1.2 for crying out loud.

Can someone please tell me what to do? I literally have NO idea where to start and the hw is due on Friday.

Thank you.
 

Answers and Replies

phyzguy
Science Advisor
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Start with problem #1. Use the homework template, show us the problem, and show us what you know and your attempts to solve it.
 
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Consider the differential equation
dy/dt=-ay+b
Where both a and b are positive numbers.
a) solve the differential equation.
b) sketch the solution for several different initial conditions.
c) describe how the solutions change under each of the following conditions:
i. a increases
ii. b increases
iii. both a and b increase, but the ratio b/a remains the same.

Okay, so looking at other examples, I see that they started out by saying that y(0)=y_0
Where y is an arbitrary number.

But now what?

I'm sorry if this is frustrating for you, but I think that I'm stressing myself out so much that I can't see the simple things.
 
11,090
4,599
Checkout the videos here at Mathispower4u as they may clear up various questions you may have:

https://dl.dropboxusercontent.com/u/28928849/Webpages/DifferentialEquationsVideoLibraryTable.htm

One thing about differential equations is that you could consider it more of an art. The equations have been categorized into various groups and for each group some mathematician has developed a recipe for solving it. This is the best approach so far and a very organized way of teaching it.

Consider when you learned about integral calculus you were given a few methods to try in order to integrate some expression. Differential equations is the next logical step above integral calculus where now the expressions are much more complex. Many of these expressions come from real world problems so the solution become very important.
 
phyzguy
Science Advisor
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1,324
Have you talked at all about methods to solve different types of differential equations? As jedishrfu said, there are different types and you need to identify what type you are dealing with to know how to approach it. This one is approached by the separation of variables method, where you try to get all of the the terms containing y on one side of the equation and all of the terms containing t on the other side. Try doing this and then see if you can see what to do next.
 
stevendaryl
Staff Emeritus
Science Advisor
Insights Author
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Consider the differential equation
dy/dt=-ay+b
Unfortunately, solving differential equations is like solving integrals (and unlike solving quadratic equations). There is no step-by-step approach that is guaranteed to always give you an answer. Instead, there is a collection of techniques for solving particular types of equations, and you have to develop an intuition about recognizing that the particular problem can be recast into a form that you know how to solve.

Here is a list of strategies:
https://en.wikipedia.org/wiki/List_of_solution_strategies_for_differential_equations
 
Stephen Tashi
Science Advisor
6,846
1,143
I am completely lost. I just started my O.D.E course this week and I'm already sinking.
Most courses in differential equations use the "dy",, "dx" approach instead of the "f'(x)" approach. Have you taken courses in physics or other disciplines where material is explained in terms of the "dy" "dx" sort of reasoning ?
 
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Expanding on what @phyzguy said, questions like this should be posted in the Homework and Coursework Problems section (in Calculus and Beyond), and using the homework template.

The Academic Guidance section is intended to address general questions about academic courses, not specific problems from those courses. If you repost this problem as described above (again, using the homework template, showing your efforts), we will help you with this question.

Thread closed.
Consider the differential equation
dy/dt=-ay+b
Where both a and b are positive numbers.
a) solve the differential equation.
b) sketch the solution for several different initial conditions.
c) describe how the solutions change under each of the following conditions:
i. a increases
ii. b increases
iii. both a and b increase, but the ratio b/a remains the same.

Okay, so looking at other examples, I see that they started out by saying that y(0)=y_0
Where y is an arbitrary number.

But now what?

I'm sorry if this is frustrating for you, but I think that I'm stressing myself out so much that I can't see the simple things.
 

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