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Homework Help
Precalculus Mathematics Homework Help
Playing With Logs while solving y-x=5(ln|y+3|-ln|x+4|) for y.
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[QUOTE="gikiian, post: 4515613, member: 322622"] [h2]Homework Statement [/h2] The problem is actually the following Separable Differential Equation: [CENTER][itex]\frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8}[/itex][/CENTER] I am required to find y(x).[b]2. Homework Equations and techniques[/b] - 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: [CENTER][itex]e^{ln|x|}=x[/itex] ; [itex]ln|xy|=ln|x|+ln|y|[/itex][/CENTER][h2]The Attempt at a Solution[/h2] [CENTER][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] [/CENTER] 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? [/QUOTE]
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Homework Help
Precalculus Mathematics Homework Help
Playing With Logs while solving y-x=5(ln|y+3|-ln|x+4|) for y.
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