# DSolve empty solution error? **URL:** \ **Category:** Questions\ **Tags:** calculus, equation-solving\ **Created:** [April 29, 2022, 10:18pm UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984 "2022-04-29T22:18:00Z")\ **Posts on this page:** 12\ **Page:** 1
**Author:** ![stephenmor](https://avatars.discourse-cdn.com/v4/letter/s/b782af/32.png) [@stephenmor](https://community.wolfram.com/u/stephenmor)\ **Post date:** [April 29, 2022, 10:18pm UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/1 "2022-04-29T22:18:00Z")
I have tried the following and get an error I don’t understand. I am a bit of a newbie so I expect there is a simple explanation. ``` DSolve[{f'[t] == k f[t] - c, f[0] == D, f[T] == 0}, f[t], t] ``` I get DSolve::bvnul: For some branches of the general solution, the given boundary conditions lead to an empty solution. I don’t understand this! please help! Many thanks, Steve ---
**Author:** ![hdolhaine](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hdolhaine/32/35924_2.png) [@hdolhaine](https://community.wolfram.com/u/hdolhaine)\ **Post date:** [April 30, 2022, 12:07am UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/2 "2022-04-30T00:07:41Z")
D is a Mathematica intrinsic symbol. You should avoid variable names with capital letters. I think ``` hh[t_] := (a (-E^(k t) + E^(k T)))/(-1 + E^(k T)) ``` With D interchanged with a is what you are looking for. ``` hh[0] hh[T] ``` ---
**Author:** ![stephenmor](https://avatars.discourse-cdn.com/v4/letter/s/b782af/32.png) [@stephenmor](https://community.wolfram.com/u/stephenmor)\ **Post date:** [April 30, 2022, 12:23am UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/3 "2022-04-30T00:23:32Z")
Many thanks ---
**Author:** ![stephenmor](https://avatars.discourse-cdn.com/v4/letter/s/b782af/32.png) [@stephenmor](https://community.wolfram.com/u/stephenmor)\ **Post date:** [April 30, 2022, 12:30am UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/4 "2022-04-30T00:30:34Z")
I tried changing the variable names but that didn’t help. ``` DSolve[{f'[t] == k f[t] - c, f[0] == s, f[p] == 0}, f[t], t] ``` Maybe I didn’t understand your suggestion. ---
**Author:** ![stephenmor](https://avatars.discourse-cdn.com/v4/letter/s/b782af/32.png) [@stephenmor](https://community.wolfram.com/u/stephenmor)\ **Post date:** [April 30, 2022, 12:38am UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/5 "2022-04-30T00:38:37Z")
Now I must also find out how to mark myself as retired! Because a I am also happily retired. ---
**Author:** ![hdolhaine](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hdolhaine/32/35924_2.png) [@hdolhaine](https://community.wolfram.com/u/hdolhaine)\ **Post date:** [April 30, 2022, 12:40am UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/6 "2022-04-30T00:40:19Z")
Well, DSolve doesn’t work on my system either, but hh given above solves the ODE and the other conditions. ---
**Author:** ![stephenmor](https://avatars.discourse-cdn.com/v4/letter/s/b782af/32.png) [@stephenmor](https://community.wolfram.com/u/stephenmor)\ **Post date:** [April 30, 2022, 12:56am UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/7 "2022-04-30T00:56:34Z")
Don’t the E^(k t) terms cancel? ---
**Author:** ![stephenmor](https://avatars.discourse-cdn.com/v4/letter/s/b782af/32.png) [@stephenmor](https://community.wolfram.com/u/stephenmor)\ **Post date:** [April 30, 2022, 12:58am UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/8 "2022-04-30T00:58:53Z")
Oh no, sorry. ---
**Author:** ![stephenmor](https://avatars.discourse-cdn.com/v4/letter/s/b782af/32.png) [@stephenmor](https://community.wolfram.com/u/stephenmor)\ **Post date:** [April 30, 2022, 1:19am UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/9 "2022-04-30T01:19:03Z")
Your solution is missing the constant ‘c’ It does give the correct boundary values. ---
**Author:** ![stephenmor](https://avatars.discourse-cdn.com/v4/letter/s/b782af/32.png) [@stephenmor](https://community.wolfram.com/u/stephenmor)\ **Post date:** [April 30, 2022, 1:27am UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/10 "2022-04-30T01:27:04Z")
In[32]:= hh[t\_] := (a (-E^(k t) + E^(k T)))/(-1 + E^(k T)) ``` In[33]:= hh[0] Out[33]= a In[34]:= hh[T] Out[34]= 0 In[35]:= hh'[t] - k hh[t] Out[35]= -((a E^(k t) k)/(-1 + E^(k T))) - ( a (-E^(k t) + E^(k T)) k)/(-1 + E^(k T)) ``` ---
**Author:** ![hdolhaine](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hdolhaine/32/35924_2.png) [@hdolhaine](https://community.wolfram.com/u/hdolhaine)\ **Post date:** [April 30, 2022, 12:18pm UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/11 "2022-04-30T12:18:13Z")
Your In[35] is not the complete differential equation. And c is fixed by your conditions. Look at ``` hh'[t] - (k hh[t] - c) /. c -> (a E^(k T) k)/(-1 + E^(k T)) // FullSimplify ``` ---
**Author:** ![hdolhaine](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/hdolhaine/32/35924_2.png) [@hdolhaine](https://community.wolfram.com/u/hdolhaine)\ **Post date:** [April 30, 2022, 12:57pm UTC](https://community.wolfram.com/t/dsolve-empty-solution-error/19984/12 "2022-04-30T12:57:17Z")
Here is the whole procedure ``` dgl = f'[t] == k f[t] - c sol = f[t] /. DSolve[dgl, f[t], t][[1, 1]] /. C[1] -> u ff[u_] := Evaluate[sol] (*ff fulfills the diff equation*) D[ff[u], t] - (k ff[u] - c) // Simplify (*you have only one constant of integration, so c is not free but must be adapted*) e1 = (ff[u] /. t -> 0) == d e2 = (ff[u] /. t -> T) == 0 sol2 = Solve[{e1, e2}, {u, c}] // Flatten gg = ff[u] /. sol2 // Simplify gg /. t -> 0 gg /. t -> T (* use the fixed c in the differential equation *) D[gg, t] - (k gg - c) /. sol2 // Simplify ```