# Thread: Ordinary Differential Equations questions (No problems)

1. ## Ordinary Differential Equations questions (No problems)

Just had a few questions that are on my mind about knowing how to tell one form from the other. The forms that we have learned are

1. Separable (Easiest)
2. Linear
3. Exact
4. Bernoulli
5. Homogeneous

Questions:

1. I know that Linear is of the form

dy/dx + P(x)y = Q(x). Given that y is the dependent variable, for this to work Q(x) cannot have any y variable correct? IF Q(x) DID have a y variable to the nth power, then it would be Bernoulli right?

2. For a D.E. to be considered Exact, it must first pass the test for exactness even though it is of the form P(x)dx + Q(x)dy = 0 correct?

3. I'm having a hard time knowing initially which method will prove to be the fastest and most efficient given some random problem in the book. Any tips or tricks you guys can let me know about?

So far that's all the questions I have. Any feedback is much appreciated.

2. Originally Posted by JonathanEyoon
1. I know that Linear is of the form

dy/dx + P(x)y = Q(x). Given that y is the dependent variable, for this to work Q(x) cannot have any y variable correct?
Right. When we write $\displaystyle Q(x)$ it immediately means that $\displaystyle Q$ is a function of variable $\displaystyle x$ only - so there is no $\displaystyle y$ term.
IF Q(x) DID have a y variable to the nth power, then it would be Bernoulli right?
I think you want to say if instead of $\displaystyle Q(x)$ we had $\displaystyle Q(x)y^n$. Yes, in that case we have a Bernoulli equation which can be turned into a first-order linear differencial equation - as above.

2. For a D.E. to be considered Exact, it must first pass the test for exactness even though it is of the form P(x)dx + Q(x)dy = 0 correct?
It needs to have the form $\displaystyle M(x,y) + N(x,y)y' = 0$ and $\displaystyle \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}$.

3. I'm having a hard time knowing initially which method will prove to be the fastest and most efficient given some random problem in the book. Any tips or tricks you guys can let me know about?
The best thing to do is to learn how to recognize what kind of differencial equation it is. Once you recognized it then you know the method to use to solve it.

3. Appreciated~ and thanks for showing me a different way to see Bernoulli.