Hope the following link may be helpful to you. It is from Matlab.

https://www.mathworks.com/help/symbolic/solve-a-single-differential-equation.html

Dear Diego Espinoza

These links might be helpful, have a look:

1. https://www.infoq.com/news/2020/12/caltech-ai-pde/

2. https://towardsdatascience.com/using-neural-networks-to-solve-ordinary-differential-equations-a7806de99cdd

3. Dearhttps://www.researchgate.net/profile/Roman-Khudorozhkov/publication/336055869_PyDEns_a_Python_Framework_for_Solving_Differential_Equations_with_Neural_Networks/inline/jsViewer/5db2c6764585155e270022bb?inViewer=1&pdfJsDownload=1&origin=publication_detail&previewAsPdf=false

Kind Regards

Qamar Ul Islam

Dear Diego Espinoza ,

Following simple code is written to solve ODE using Euler's Method -

import math as m

def PRA_EM(fun,x0,y0,xn,n):

h=(xn-x0)/n

for i in range(n+1):

xi=x0+i*h

print("x = %.4f"%xi,"y = %.4f"%y0)

ynew=y0+h*fun(x0+i*h,y0)

y0=ynew

-------------------------------------------------------------------------------------------------------------------

Sample input/example to execute the program:

PRA_EM(lambda x,y: x+y,0,1,1,5)

Researching, I found documentation on the subject, plus a repository on Git-Hub, I mean DeepXDE, this is a deep learning library on TensorFlow, the authors are Lu, Lu and Meng, Xuhui and Mao, Zhiping and Karniadakis, George Em.

According to its documentation it can be used if you need to perform the following tasks.

• solves forward and inverse partial differential equations (PDEs) via physics-informed neural network (PINN),
• solves forward and inverse integro-differential equations (IDEs) via PINN,
• solves forward and inverse fractional partial differential equations (fPDEs) via fractional PINN (fPINN),
• approximates functions from multi-fidelity data via multi-fidelity NN (MFNN),
• approximates nonlinear operators via deep operator network (DeepONet),
• approximates functions from a dataset with/without constraints.

Attached is the repository page and the document referred to it.

Thank you very much for your answers

https://deepxde.readthedocs.io/en/latest/#

https://github.com/lululxvi/deepxde

I have an example in PyTorch: Burger's equation