Re: solving simultaneous coupled differential equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg62704] Re: solving simultaneous coupled differential equations*From*: dh <dh at metrohm.ch>*Date*: Fri, 2 Dec 2005 05:53:03 -0500 (EST)*References*: <dmlvm8$m95$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, here is a simple example: we replace one 5th order lin DEQ by 5 first order lin DEQ: we have y'''''[x] == 0 for testing, the solution of this is y[x]= c0 + c1 x + x2 x^2 + c3 x^3+c4 x^4 from this we can get 5 coupled lin DEQ by replacing derivatives by new functions y by y0 y' by y1 .. y'''' by y4 with this we get the following 5 lin DEQ: eq={ y0'[x]==y1[x], y1'[x]==y2[x], y2'[x]==y3[x], y3'[x]==y4[x], y4'[x]==0 }; this can be solved like this: var = {y0, y1, y2, y3, y4}; DSolve[eq, var, x] this yields for y0: C[1] + x*C[2] + (x^2*C[3])/2 + 35*C[4] + (x^3*C[4])/6 + 15*(C[3] + x*C[4]) + 5*(C[2] + x*C[3] + (x^2*C[4])/2) note that the constants are different ci != c[i] but we can verify that this has the above form by: Collect[...,x] Daniel akgsh at yahoo.com wrote: > Hi, > i am trying to solve 5 coupled first order differential equations.is > there any way to solve this using mathematica.please help with > necessary steps. > thanks > kumar >