How to solve the following differential equation? y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r where c1, c2, c3 are constants... and r is a non-integer Thanks!
How to solve the following differential equation?
Started by ●May 18, 2007
Reply by ●May 18, 20072007-05-18
On May 18, 12:01 am, "Mike" <meathea...@gmail.com> wrote:> How to solve the following differential equation? > > y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r > > where c1, c2, c3 are constants... and r is a non-integer > > Thanks!That looks integrable to me.
Reply by ●May 18, 20072007-05-18
In article <f2jivp$296$1@news.Stanford.EDU>, "Mike" <meatheadIV@gmail.com> writes: > >How to solve the following differential equation? > > >y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r > > > >where c1, c2, c3 are constants... and r is a non-integer > > > >Thanks! > > > no numerical solution without initial value: ask Maple, Mathematica or look here Kamke: Differetialgleichungen , Loesungsmethoden und Loesungen hth peter
Reply by ●May 18, 20072007-05-18
>> How to solve the following differential equation? >> >> y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r >> >> where c1, c2, c3 are constants... and r is a non-integer >> >> Thanks! > >That looks integrable to me.All he needs is to learn how to do y log y via integration by parts -- ciao, Bruce drift wave turbulence: http://www.rzg.mpg.de/~bds/
Reply by ●May 18, 20072007-05-18
"Peter Spellucci" <spellucci@fb04373.mathematik.tu-darmstadt.de> wrote in message news:f2kdk4$vi$1@fb04373.mathematik.tu-darmstadt.de...> > In article <f2jivp$296$1@news.Stanford.EDU>, > "Mike" <meatheadIV@gmail.com> writes: > > > >How to solve the following differential equation? > > > > > >y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r > > > > > > > >where c1, c2, c3 are constants... and r is a non-integer > > > > > > > >Thanks! > > > > > > > no numerical solution without initial value: > ask Maple, Mathematica or look here > Kamke: Differetialgleichungen , > Loesungsmethoden und Loesungen > > hth > peterBefore numerical stuff, is it possible for closed-form solution? Thanks!
Reply by ●May 18, 20072007-05-18
"Bruce Scott TOK" <Use-Author-Supplied-Address-Header@[127.1]> wrote in message news:200705181442.l4IEgcIL019059@ipp.mpg.de...>>> How to solve the following differential equation? >>> >>> y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r >>> >>> where c1, c2, c3 are constants... and r is a non-integer >>> >>> Thanks! >> >>That looks integrable to me. > > All he needs is to learn how to do y log y via integration by parts > > -- > ciao, > Bruce > > drift wave turbulence: http://www.rzg.mpg.de/~bds/ >How? Sorry I am a little bit rusty in these stuff... could you elaborate more?
Reply by ●May 18, 20072007-05-18
"Mike" <meatheadIV@gmail.com> writes:> > How to solve the following differential equation? > > > y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r > > > > where c1, c2, c3 are constants... and r is a non-integerSymbolically or numerically? It's a separable DE, but the integral won't have a closed form in general, even if r was an integer > 1. Numerically, the usual methods should have no trouble with it. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada
Reply by ●May 18, 20072007-05-18
In article <200705181442.l4IEgcIL019059@ipp.mpg.de>, Bruce Scott TOK <Use-Author-Supplied-Address-Header@[127.1]> writes: >>> How to solve the following differential equation? >>> >>> y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r >>> >>> where c1, c2, c3 are constants... and r is a non-integer >>> >>> Thanks! >> >>That looks integrable to me. > >All he needs is to learn how to do y log y via integration by parts > >-- >ciao, >Bruce > >drift wave turbulence: http://www.rzg.mpg.de/~bds/ > ??? int(1/(c1*y*log(y)+c2*y+c3*y^r) dy ) = ??? sorry peter
Reply by ●May 18, 20072007-05-18
Mike wrote:>"Bruce Scott TOK" <Use-Author-Supplied-Address-Header@[127.1]> wrote in >message news:200705181442.l4IEgcIL019059@ipp.mpg.de... >>>> How to solve the following differential equation? >>>> >>>> y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r >>>> >>>> where c1, c2, c3 are constants... and r is a non-integer >>>> >>>> Thanks! >>> >>>That looks integrable to me. >> >> All he needs is to learn how to do y log y via integration by parts>How? Sorry I am a little bit rusty in these stuff... could you elaborate >more?Actually, it looks perhaps easier to divide through by y and then relabel x = log y, so that x' = c1*x + c2 + c3 exp[ (r-1) x ] where x=x(t) As the other poster says, you can set up the integral for t as a function of x but that's as far as it goes analytically (i.e., "reduce the problem to quadratures"). -- ciao, Bruce drift wave turbulence: http://www.rzg.mpg.de/~bds/
Reply by ●May 18, 20072007-05-18
On May 18, 7:42 am, Bruce Scott TOK <Use-Author-Supplied-Address- Header@[127.1]> wrote:> >> How to solve the following differential equation? > > >> y'(t) = c1*y(t)*log(y(t)) + c2*y(t) + c3*(y(t))^r > > >> where c1, c2, c3 are constants... and r is a non-integer > > >> Thanks! > > >That looks integrable to me. > > All he needs is to learn how to do y log y via integration by partsIs it easy to integrate 1/[y log y + a y + b y^r]? I don't think so, at least not for general r. R.G. Vickson> > -- > ciao, > Bruce > > drift wave turbulence: http://www.rzg.mpg.de/~bds/
