       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, f=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:=
g=DSolve[{a*Derivative[f][x] + Derivative[f][x] == Derivative[1=
]
[h][x], f == 0, f == 1}, f[x], x]

Out=
{
{f[x] -> 1 + Integrate[(E^(1/a - K\$1739/a)*(1 + Integrate[Integrate
[(E^(K\$1718/a)*Derivative[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[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:=
g /. {K\$3425 -> K, K\$3404 -> K}

Out=
{
{f[x] -> 1 + Integrate[(E^(1/a - K/a)*(1 + Integrate[Integrate[(E^
(K/a)*Derivative[h][K])/a, {K, 1, K}]/
E^(K/a), {K, 1, 0}]))/(a*(-1 + E^(1/a))) + Integrate
[(E^(K/a)*Derivative[h][K])/a, {K, 1, K}]/
E^(K/a), {K, 1, x}]}}

Regards
Dimitris Anagnostou

```

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