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Help with finding asymptote: dy/dx = 2y - 4x
- Thread starter bobers
- Start date
bobers said:I have a function dy/dx=2y-4x
I need to find the equation of any asymptotes
Don't know where to start
If it has an asymptote that is a line, say y=mx+c, then dy/dx=m. Now sub these into the DE, and find m and c.
bobers said:Then would it be
y=(2y-4x)x+C ?
No. Sorry for the confusion. There are two functions here
* the curve given by y'=2y-4x
* the asymptote, given by y=mx+c.
Near the asymptote, both of these are almost the same - the curve's values approach the asymptote's values. The curve's slope approaches the asymptote's slope.
Therefore, in the limit, y=mx+c, y'=m,.... and y'=(2y-4x). If you substitute your expressions for y and y' into the DE, there'll be no more y's. The left hand side and right hand side must be equal for all x, m and c are constants and don't depend on x.