Differential Equations Help

  • Thread starter rpgkevin
  • Start date
  • #1
4
0

Homework Statement


Solve The following Equations:
2(y+3)dx-xydy=0

(x2-xy+y2)dx - xydy=0 use following assumption y=vx

xy3+ex2dy=0

The Attempt at a Solution



I am still a novice at diff eqs but here is what I got on the first one:
After seperating it I ended up with
(dx/x)=(ydy)/(2y+6) Then I get stuck with integrating the side with the Y

For the other two I believe they can not be separated and I am not sure what to do when this is the case
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
For the right side, you can rewrite it as

y/2(y+3) dy or ½(y+3-3)/(y+3), you can simply it even further i.e. polynomial division
 
  • #3
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,845
1,416
For the y-integral on the first one, you can do this:[tex]\frac{1}{2}\int \frac{y}{y+3}\,dy = \frac{1}{2}\int \frac{(y+3)-3}{y+3}\,dy = \frac{1}{2}\int \left[1-\frac{3}{y+3}\right]\,dy[/tex]or you could use the substitution u=y+3.

On the second one, what did you get when you used the substitution y=vx?
 
  • #4
4
0
For the y-integral on the first one, you can do this:[tex]\frac{1}{2}\int \frac{y}{y+3}\,dy = \frac{1}{2}\int \frac{(y+3)-3}{y+3}\,dy = \frac{1}{2}\int \left[1-\frac{3}{y+3}\right]\,dy[/tex]or you could use the substitution u=y+3.

On the second one, what did you get when you used the substitution y=vx?
I have never used the substitution method I have no clue how to use that I looked it up earlier because someone told me that but I was unable to use the examples to work that one out
 
  • #6
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,845
1,416
I have never used the substitution method I have no clue how to use that I looked it up earlier because someone told me that but I was unable to use the examples to work that one out
If you differentiate y=vx with respect to x, you'll get
[tex]\frac{dy}{dx} = v + x\frac{dv}{dx}[/tex]
Multiplying through by dx, you end up with
[tex]dy = v \,dx + x\, dv[/tex]
Use this and the original substitution to eliminate y from the original equation. You should find it separates then, allowing you to solve for v, from which you can then find y.
 
  • #7
4
0
I don't think you wrote this correctly - there seems to be a dx missing.
ahh you are correct it is suppose to be a dx after the xy3
 
  • #8
4
0
If you differentiate y=vx with respect to x, you'll get
[tex]\frac{dy}{dx} = v + x\frac{dv}{dx}[/tex]
Multiplying through by dx, you end up with
[tex]dy = v \,dx + x\, dv[/tex]
Use this and the original substitution to eliminate y from the original equation. You should find it separates then, allowing you to solve for v, from which you can then find y.
I tried what you said and plugged stuff back in and then I Tried separating things out and I cant seem to get it to separate out I am stuck at
X2(1-V-V2)dx=x2v2+(x3v)dv/dx)
 
  • #9
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,845
1,416
Please show your work. It's impossible to see what went wrong without seeing what you actually did.
 
  • #10
HallsofIvy
Science Advisor
Homework Helper
41,833
961
For (2) you are told to let y= vx and from that dy= vdx+ xdv. Replace y and dy in the equation with those. It will reduce to a separable equation.
 
  • #11
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,845
1,416
ahh you are correct it is suppose to be a dx after the xy3
In that case, it's pretty straightforward to see the equation separates. Why do you think it can't be separated?
 
  • #12
34,533
6,229
Also, when the variables are separated, the integration is not very difficult.
 

Related Threads on Differential Equations Help

  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
5
Views
924
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
2
Views
927
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
3
Views
733
  • Last Post
Replies
2
Views
752
  • Last Post
Replies
4
Views
988
  • Last Post
Replies
2
Views
969
  • Last Post
Replies
1
Views
1K
Top