Re: How to get the best expression of an ode's solution

*To*: mathgroup at smc.vnet.net*Subject*: [mg93639] Re: How to get the best expression of an ode's solution*From*: dimitris <dimmechan at yahoo.com>*Date*: Wed, 19 Nov 2008 05:40:26 -0500 (EST)*References*: <gfuc0q$ei9$1@smc.vnet.net>

On 18 =CD=EF=DD, 14:21, catny <d... at shu.edu.cn> wrote: > Hello everyone > > Here is a linear ODE > a f''[x]+f'[x]==h'[x] > with f[0]=0, f[1]=1 > It is easy to solve it by Mathematica, but the expression is complex. How= to get it's simplest form? > > Thanks I don't see a simpler form unless you specify the function h[x]. On my 5.2 version I get In[3]:= g=DSolve[{a*Derivative[2][f][x] + Derivative[1][f][x] == Derivative[1= ] [h][x], f[0] == 0, f[1] == 1}, f[x], x] Out[3]= { {f[x] -> 1 + Integrate[(E^(1/a - K$1739/a)*(1 + Integrate[Integrate [(E^(K$1718/a)*Derivative[1][h][K$1718])/a, {K$1718, 1, K$1739}]/E^(K$1739/a), {K$1739, 1, 0}]))/(a* (-1 + E^(1/a))) + Integrate[(E^(K$1718/a)*Derivative[1][h][K$1718])/a, {K$1718, 1, K$1739}]/E^(K$1739/a), {K$1739, 1, x}]}} K$ variables are used as dummy integration variables. Perhaps something like the following might help you In[8]:= g /. {K$3425 -> K[1], K$3404 -> K[2]} Out[8]= { {f[x] -> 1 + Integrate[(E^(1/a - K[1]/a)*(1 + Integrate[Integrate[(E^ (K[2]/a)*Derivative[1][h][K[2]])/a, {K[2], 1, K[1]}]/ E^(K[1]/a), {K[1], 1, 0}]))/(a*(-1 + E^(1/a))) + Integrate [(E^(K[2]/a)*Derivative[1][h][K[2]])/a, {K[2], 1, K[1]}]/ E^(K[1]/a), {K[1], 1, x}]}} Regards Dimitris Anagnostou