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;
and
Show that ifdoes not equal
or
, then the substitution
reduces Bernoulli's equation to a linear equation.
Bernoulli's Equation Standard Formy = q(t)y^n)
;
(Linear)
![e^{2\epsilon t}[v' + 2\epsilon v] = 2\sigma e^{2\epsilon t}](http://latex.codecogs.com/png.latex?e^{2\epsilon t}[v' + 2\epsilon v] = 2\sigma e^{2\epsilon t})
![\frac{dv}{dt}[e^{2\epsilon t}v] = 2\sigma e^{2\epsilon t}](http://latex.codecogs.com/png.latex?\frac{dv}{dt}[e^{2\epsilon t}v] = 2\sigma e^{2\epsilon t})
![\int dv[e^{2\epsilon t}v] = \int [2\sigma e^{2\epsilon t}]dt](http://latex.codecogs.com/png.latex?\int dv[e^{2\epsilon t}v] = \int [2\sigma e^{2\epsilon t}]dt)
![e^{2\epsilon t}v = 2\sigma \int e^{2\epsilon t}dt \rightarrow e^{2\epsilon t}v = 2\sigma \left[\frac{e^{2\epsilon t}}{2\epsilon}}\right]](http://latex.codecogs.com/png.latex?e^{2\epsilon t}v = 2\sigma \int e^{2\epsilon t}dt \rightarrow e^{2\epsilon t}v = 2\sigma \left[\frac{e^{2\epsilon t}}{2\epsilon}}\right])
The books answer was
My answer's not even close, can someone walk me through this problem so I can see what I did wrong?
