# Adding set of equations in ModelingToolkit

**URL:** <https://discourse.julialang.org/t/adding-set-of-equations-in-modelingtoolkit/100019>\
**Category:** General Usage\
**Tags:** question, modelingtoolkit, diferential-equation\
**Created:** [June 7, 2023, 7:49pm UTC](https://discourse.julialang.org/t/adding-set-of-equations-in-modelingtoolkit/100019 "2023-06-07T19:49:13Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![Ethan\_Tran](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ethan_tran/32/49198_2.png) [@Ethan\_Tran](https://discourse.julialang.org/u/Ethan_Tran)\
**Post date:** [June 7, 2023, 7:49pm UTC](https://discourse.julialang.org/t/adding-set-of-equations-in-modelingtoolkit/100019/1 "2023-06-07T19:49:13Z")

</div>

I have several sets of differential equations, and to reduce the time of implementation I try to implement each set of equations by for loop as below (just for example):

```julia
@variable (x(t))[1:n] (y(t))[1:n]
eq1 = [0 ~ D(x[i]) + x[i] - y[i] for i in 1:n]
eq2 = [0 ~ D(y[i]) + sin(x[i]) + x[i] - cos(y[i]) for i in 1:n]

```

To create an ODE system it is needed to add all sets of equations as one.  
Please help me with how could I accumulate eq1 and eq2 into one set.  
Thank you.

---

<div class="post-metadata">

**Author:** ![baggepinnen](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/baggepinnen/32/693_2.png) [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)\
**Post date:** [June 7, 2023, 7:55pm UTC](https://discourse.julialang.org/t/adding-set-of-equations-in-modelingtoolkit/100019/2 "2023-06-07T19:55:05Z")

</div>

```julia
[eq1; eq2]

```