- #1
gikiian
- 98
- 0
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]
[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: