Number of results: 11
See the practical steps listed here for the first order linear equation. http://www.sosmath.com/diffeq/first/lineareq/lineareq.html
Thursday, January 29, 2009 at 11:31pm by bobpursley
The page at http://www.sosmath.com/diffeq/first/phaseline/phaseline.html has quite a lengthy and clear discussion of phase lines and equilibrium points. Part (b) wants you to solve the equation analytically and compare the solution with your qualitative analysis in part (a).
Sunday, February 3, 2013 at 2:51pm by Steve
Thursday, January 29, 2009 at 11:30pm by bobpursley
maths-urgently needed[Differential equations]
Looks like a Riccati equation. Standard methods, such as those at http://www.sosmath.com/diffeq/first/riccati/riccati.html will lead to the solution y = xe^(x^2) / (cx + e^(x^2) - πix erf(ix)) where erf(x) is the error function.
Thursday, February 7, 2013 at 10:13am by Steve
This is a first order linear differential equation and can be solved by the "integrating factor" method. See http://www.sosmath.com/diffeq/first/lineareq/lineareq.html
Monday, August 11, 2008 at 1:52pm by drwls
Well by inspection, dx/dt=-.3/2 x^2 - 1/2((x-1)^2+ a^2)^.5+1/2 (((x+1)^2+a^2)^.5 and then x= -1/20x^3- 1/3 ((x-1)^2+ a^2)^3/2 + you finish it. Did I miss something?
Wednesday, March 25, 2009 at 1:55pm by bobpursley
how do i find the bifurcation for this: d^x/dt^2 = -.3 x - (x - 1)/((x - 1)^2 + a^2)^(3/2) - (x + 1)/((x + 1)^2 + a^2)^(3/2) we've tried using mathematica but it just runs forever...
Wednesday, March 25, 2009 at 1:55pm by Mischa
d/dx (x)(e^xy)(cos2x). Product rule lets me take the derivative of f(x)g(x). But three functions?
Friday, February 11, 2011 at 7:27pm by Dave
linear analysis (differential equation)
As BobPursley and I explained in our previous answer, what you have is a first order linear differential equation. The general form of this type of differential equation is dy/dx = P(x)*y + Q(x) In your case, P(x) = 1, and Q(x) = x The procedure for obtaining a general ...
Wednesday, August 20, 2008 at 1:56am by drwls
Let P(t) represent the population of a non-native species introduced to a new area for the purposes of harvesting. Suppose we intially introduce P0 = 100 indicidcuals and suppose the population grows exponentially with growth-rate coefficient k=2 if there is no harvesting (for...
Sunday, February 22, 2009 at 9:27pm by Mischa
Suppose a species of fish in a particular lake has a population that is modeled by the logistic population model with growth rate k, carrying capacity N, and time t measured in years. Suppose the growth-rate parameter k=.3 and the carrying capacity N=2500. Suppose P(0)=2500. (...
Wednesday, February 4, 2009 at 5:05pm by Mischa