- #1
JNBirDy
- 38
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Homework Statement
Find an implicit, general solution to:
dy/dx = (6x - 4y) / (x - y) with x > 0.
Homework Equations
The Attempt at a Solution
dy/dx = (6x - 4y) / (x - y)
x(dv/dx) + v = (6 - 4v) / (1 - v)
[(1-v) / (v-3)(v-2)] dv = dx / x
[itex]\int dv/(v-2)[/itex] - 2[itex]\int dv/(v-3)[/itex] = [itex]\int dx/x[/itex]
ln|v-2| -2ln|v-3| + C[itex]_{1}[/itex] = ln|x| + C[itex]_{2}[/itex]
ln|v-2| -2ln|v-3|- ln|x| = C[itex]_{3}[/itex]
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Not sure where to go from here, I'm trying to get it into the form
|y - ax| / (y - bx)^c = C, for some constants a, b, c, and C.
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Any help is appreciated, thanks.