# ODE solver giving wrong results
**URL:** https://discourse.julialang.org/t/ode-solver-giving-wrong-results/63891
**Category:** General Usage
**Tags:** diffeq
**Created:** [July 1, 2021, 2:04pm UTC](https://discourse.julialang.org/t/ode-solver-giving-wrong-results/63891 "2021-07-01T14:04:06Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@rodpiferreira](https://discourse.julialang.org/u/rodpiferreira)
#### Post date: [July 1, 2021, 2:04pm UTC](https://discourse.julialang.org/t/ode-solver-giving-wrong-results/63891/1 "2021-07-01T14:04:06Z")
Hey everyone!
I want to solve f(u,p,t) = An\*u + b, where:
An = [0.0+0.0im 1.0+0.0im
5.0+0.0im -1.0+0.0im],
b = [1.0+0.0im, 0.0+0.0im],
x = [0.0+0.0im, 1.0+0.0im] (initial condition)
Which means that I have a system like this:
x’ = y+1, x(0) = 0
y’ = 5x-y, y(0) = 1
And I get the following ODE: x"(t)+x’(t)-5x(t)=1. The analytic solution gives me x(1) = 3.1259897764930082
However, when I solve it via Julia’s ODE solver, I get x(1) = 4.21229.
Am I missing something? Here’s my code:
```julia
An = [0.0+0.0im 1.0+0.0im
5.0+0.0im -1.0+0.0im]
b = [1.0+0.0im, 0.0+0.0im]
x = [0.0+0.0im, 1.0+0.0im]
tspan = (0.0,1.0)
f(u,p,t) = An*u + b;
prob = ODEProblem(f, x, tspan)
sol = solve(prob, Vern7(), dt = 0.1, adaptive = false, reltol=1e-8)
```
---
### Author:  [@Salmon](https://discourse.julialang.org/u/Salmon)
#### Post date: [July 1, 2021, 2:38pm UTC](https://discourse.julialang.org/t/ode-solver-giving-wrong-results/63891/2 "2021-07-01T14:38:56Z")
Seems strange, when I simply copy and paste your code, i get
```julia
julia> sol = solve(prob, Vern7(), dt = 0.1, adaptive = false, reltol=1e-8);
julia> sol(1)
2-element Vector{ComplexF64}:
3.125989776501887 + 0.000000000000000im
5.058513100378909 + 0.000000000000000im
julia>
```
which corresponds well enough to your analytical solution
---
### Author:  [@Salmon](https://discourse.julialang.org/u/Salmon)
#### Post date: [July 1, 2021, 2:58pm UTC](https://discourse.julialang.org/t/ode-solver-giving-wrong-results/63891/3 "2021-07-01T14:58:57Z")
Another thing even though unrelated to your original problem: Setting `adaptive = false`, should basically invalidate your `reltol = 1e-8` option, since the ODE solver is only allowed to go in steps of 0.1 without adjusting the stepsize due to error. It should always be safer to use the default, which is `adaptive = true`.
---
### Author:  [@BLI](https://discourse.julialang.org/u/BLI)
#### Post date: [July 1, 2021, 3:07pm UTC](https://discourse.julialang.org/t/ode-solver-giving-wrong-results/63891/4 "2021-07-01T15:07:53Z")
The analytic solution to your equation is
x(t) = \frac{1-\sqrt{21}}{10}\exp{\left(-\frac{1+\sqrt{21}}{2}t\right)} + \frac{1+\sqrt{21}}{10}\exp{\left( \frac{\sqrt{21}-1}{2}t\right)} - \frac{1}{5}
which gives x(0) = 0 and x(1) \approx 3.1259....
Two comments:
- Why do you use complex numbers in `An`, `b`, and `x` (initial value)?
- The solution represents an unstable system, where numerical errors easily can “explode”.
---
### Author:  [@rodpiferreira](https://discourse.julialang.org/u/rodpiferreira)
#### Post date: [July 3, 2021, 3:51am UTC](https://discourse.julialang.org/t/ode-solver-giving-wrong-results/63891/5 "2021-07-03T03:51:31Z")
Thank you for replying.
Yes, I tried again later, and I got the same result this time. I guess that was a bug or something.
---
### Author:  [@rodpiferreira](https://discourse.julialang.org/u/rodpiferreira)
#### Post date: [July 3, 2021, 3:56am UTC](https://discourse.julialang.org/t/ode-solver-giving-wrong-results/63891/6 "2021-07-03T03:56:29Z")
Thanks!
I’m using complex numbers only because the other parts of my code require complex inputs.
Also, yes - I’m mainly focusing on stable systems to get lower errors (which is not this case though).