1. Differential Equation

I was having trouble with this question as I'm not sure how to split it into dy and dx in order to integrate.

x*dy/dx+y = x given y(-1)=2
.
y= ?

2. You solve it using integrating factor

3. songoku,

I'm not sure what you mean by that. I need to see what you do for the first step thanks.

4. $\displaystyle x \frac{dy}{dx} + y = x$

$\displaystyle \frac{dy}{dx} + \frac{y}{x} = 1$

Have you learnt how to solve linear form differential equation using integrating factor?

5. $\displaystyle y'+\frac{y}{x}=1$

$\displaystyle \mu{(x)}=e^{\int{\frac{1}{x}}dx}\Rightarrow\mu{(x) }=x$

Multiply both sides by your integrating factor and integrate...

$\displaystyle \int{(yx)'}=\int{x}$

$\displaystyle yx=\frac{x^{2}}{2}+c$

Solve for C

$\displaystyle 2(-1)=\frac{(-1)^{2}}{2}+C$

$\displaystyle C=-\frac{5}{2}$

Now, solve for y ($\displaystyle f(x)$) and you are done.

$\displaystyle f(x)=\frac{x}{2}-\frac{5}{2x}$

Seems like you have never been introduced to this method, so check out this wiki page: Integrating factor - Wikipedia, the free encyclopedia

It's pretty straight forward, just takes some practice.

6. Thanks songoku and Danneedshelp,

I haven't come across any questions were x and y weren't products so this is new to me. I'll have a look at the link Danneedshelp. Thanks.

7. Danneedshelp,

I've read this link and I'm still stuck with this question, I have followed your working but I'm afraid I can't see how you got the answer. I was wondering if you or another member could show me again as this question is coming up repeatedly and I'm still clueless on to do an intergrading factor.

Thanks.

http://www.mathhelpforum.com/math-he...-tutorial.html

9. Danneedshelp,

I found y=x^2/2+3/2, to be my final answer as I divided by x and then found the constant, I'm not sure which way this should happen?

Thanks.

There's typo in Danneedshelp post, the solution should be $\displaystyle f(x)=\frac{x}{2}-\frac{5}{2x}$

Can you please post your work so I can take a look at it ? ^^

11. Songoku,

I see where I went wrong with my working, I tried to cross multiply when I got to y=x/2+c/x. If I solve c from this step then I can the same answer you mentioned. (I attached my working below)

Thanks.

12. Originally Posted by songoku

There's typo in Danneedshelp post, the solution should be $\displaystyle f(x)=\frac{x}{2}-\frac{5}{2x}$

Can you please post your work so I can take a look at it ? ^^

13. songoku and Danneedshelp,

I have come across this question a few times in my reviews and I have entered this answer several times and I keep getting the question wrong and I'm not sure why? The question mentions parenthesizing the denominator carefully but I have two dominators which leads me to believe that the answer I have been entering is incorrect or that it needs rearranging of some kind.

Thanks.

A perfectly good answer, already given, is $\displaystyle y = \frac{x}{2} - \frac{5}{2x}$.
I'll bet that whoever gave you this question wants the answer written as $\displaystyle y = \frac{x^2 - 5}{2x}$, which is completely pointless since the point of the question, I would have thought, is to test whether you can solve a DE, not whether you can read the (narrow and small) mind of someone.