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Playing With Logs while solving y-x=5(ln|y+3|-ln|x+4|) for y.

  • Thread starter gikiian
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  • #1
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Homework Statement



The problem is actually the following Separable Differential Equation:
[itex]\frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8}[/itex]​
I am required to find y(x).


2. Homework Equations and techniques

- factorization (applied on the numerator and the denominator in the problem equation)
- basic integration (applied after separating the variables)
- at least the following logarithmic identities:
[itex]e^{ln|x|}=x[/itex] ; [itex]ln|xy|=ln|x|+ln|y|[/itex]​


The Attempt at a Solution



[itex]\frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8}[/itex]

[itex](1-\frac{5}{y+3})dy=(1+\frac{5}{x+4})dy[/itex]

[itex]y-5ln|y+3|=x+5ln|x+4|+C[/itex]

[itex]y-x=5(ln|y+3|-ln|x+4|)[/itex]


I also put this result in Wolfram Alpha, but it could not solve the equation for y. My instructor apparently believes that an y=f(x) can be obtained. Is there any way to do so?
 
Last edited:

Answers and Replies

  • #2
haruspex
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You appear to have a sign wrong in the middle two equations, but since it comes out right at the end maybe this was a copying out error.
i don't see a way to get it into y = f(x) form either.
 

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