Are They Symmetric With Respect To The Origin? (C) Draw A Direction Field And Some Integral Curves.

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Homogenous Diff. Eqn

• Thread starter aznkid310
• Start date Apr 15, 2008

Homework Statement

dy/dx = (x + 3y)/(x - y)

A) Solve the Differential Eqn
B) Draw a Direction Field and some integral curves. Are they symmetric w/ respect to the origin?

Homework Equations

I believe i solved the equation correctly, simply i dont know how to draw the direction fields and integral curves. I tried plotting y 5. y' in order to create the resulting direction field and integral curves, but i dont know what it looks like.

*Also, how practise I integrate the left side? I merely used an online reckoner to go the answer, simply i would similar to know how to solve this

The Attempt at a Solution

A) Afterward dividing by 10 and substituting v = y/x:

(one + 3v)/(one - v) = 15' + 5

v' = (1/x)( (one + 3v)/(1 - five) - v )

* (one-3v)/(one+3v) - 1/v dv = dx/10

After integrating and solving for c:

C = (2/3)ln(3y/x + 1) - y/10 -ln(y/10) - ln(x)
Also, y = -x

Answers and Replies

* Use long division: [tex]\frac{ane-3v}{1+3v}=-1+\frac{2}{1+3v}[/tex] then

[tex]\int \left(\frac{1-3v}{ane+3v}-\frac{i}{v}\correct)\, dv = \int \left(-1+\frac{2}{1+3v}-\frac{1}{five}\right)\, dv = -5+{\textstyle\frac{2}{iii}} \ln |1+3v| -\ln |5|+C[/tex]​

A direction field (a.k.a http://mathworld.wolfram.com/SlopeField.html" [Broken], see link for a meliorate definition) is a plot of unit of measurement vectors with slope determined by the DE (eastward.g., on our direction field at (5,1) we plot a unit vector with a slope of [itex]y^{\prime}=\frac{5+3}{five-1}= ii[/itex]).

An http://mathworld.wolfram.com/IntegralCurve.html" [Broken] is a particular solution to a differential equation corresponding to a specific value of the equation's costless parameters.

Last edited past a moderator: May 3, 2017

Hey guys!

Isn't it (1 - v)dv/(1 + five)² ?

Thanks tiny-tim.
Oops ...

[tex]x\frac{dv}{dx}=\frac{i+3v}{1-v}-v[/tex]
[tex] \frac{1-v}{(ane+v)^2}dv = \frac{dx}{x}[/tex]

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