# Setting up differential equations

**URL:** <https://discourse.julialang.org/t/setting-up-differential-equations/62120>\
**Category:** New to Julia\
**Tags:** question, diffeq\
**Created:** [May 31, 2021, 9:08am UTC](https://discourse.julialang.org/t/setting-up-differential-equations/62120 "2021-05-31T09:08:42Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![Deepa](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/deepa/32/23385_2.png) [@Deepa](https://discourse.julialang.org/u/Deepa)\
**Post date:** [May 31, 2021, 9:08am UTC](https://discourse.julialang.org/t/setting-up-differential-equations/62120/1 "2021-05-31T09:08:42Z")

</div>

I’ve the following function

```julia
function fun(dx,x,p,t)
    dx[:,:] .= mat1*x + mat2*x
end

```

Here, I’d like to scale `mat1*x + mat2*x` by the values present in a vector `scale`.

In MATLAB I would do `(1./scale).*(mat1*x + mat2*x)`. I’m not sure how element wise scaling is done in Julia for performing matrix vector multiplication.

`mat1 is of size (10 x 10) , x : (10 x 1) scale : (10 x 1)`

Suggestions?

@ptoche Could you please help me with this?

Example:

```julia

using DifferentialEquations, BenchmarkTools

mat1=[
       1 -2 1 0 0 0 0 0 0 0;
       0 1 -2 1 0 0 0 0 0 0;
       0 0 1 -2 1 0 0 0 0 0;
       0 0 0 1 -2 1 0 0 0 0;
       0 0 0 0 1 -2 1 0 0 0;
       0 0 0 0 0 1 -2 1 0 0;
       0 0 0 0 0 0 1 -2 1 0;
       0 0 0 0 0 0 0 1 -2 1;
       ];

mat2 = [
        1 -1 0 0 0 0 0 0 0 0;
        0 1 -1 0 0 0 0 0 0 0;
        0 0 1 -1 0 0 0 0 0 0;
        0 0 0 1 -1 0 0 0 0 0;
        0 0 0 0 1 -1 0 0 0 0;
        0 0 0 0 0 1 -1 0 0 0;
        0 0 0 0 0 0 1 -1 0 0;
        0 0 0 0 0 0 0 1 -1 0;
        ];

x0 = [1.0,0,0,0,0,0,0,0,0,0]
scale= [1 2 3 2 3 1 2 3];
saveat = 0:0.01:5

function fun(dx,x,p,t)
    dx[1,:] .= 0
    dx[2:9,:] .= (1/scale)*(mat1*x + mat2*x)
    dx[10,:] .= 2*(x[end-1] - x[end])
end

prob = ODEProblem(fun,x0,(0.0,5.0))
sys = modelingtoolkitize(prob)
fastprob = ODEProblem(sys,x0,(0.0,5.0),jac=true)

# Explicit RK Methods
@btime sol = solve(fastprob,Tsit5()) # 16.700 μs (245 allocations: 40.28 KiB)

```

doesn’t run successfully.

Should I do `vecdot(1/scale, mat1*x+mat2*x)` ?

---

<div class="post-metadata">

**Author:** ![ptoche](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ptoche/32/23554_2.png) [@ptoche](https://discourse.julialang.org/u/ptoche)\
**Post date:** [May 31, 2021, 10:27am UTC](https://discourse.julialang.org/t/setting-up-differential-equations/62120/2 "2021-05-31T10:27:15Z")

</div>

> [@Deepa](#):
>
> `(1./scale).*(mat1*x + mat2*x)`

Do you mean `(mat1+mat2)*x./scale` ? Try it in the REPL with 2 by 2 matrices and a simple x vector to see if that’s what you want, before throwing it into the `ODEProblem`. 🤔

You can also play around with `(one(10)./scale)` and similar.