You could start having a look to this question on RG:

https://www.researchgate.net/post/Can_anybody_suggest_me_the_best_software_for_Partial_Differential_Equations_PDEs

Dear Akhil,

You could try using the free software called Python, which is what I often use to check my solutions. If you type in a little code, it will solve quite complicated ODEs, although some solutions will be approximated versions for ODEs that cannot be written in terms of closed form elementary functions. For example, if you type out (or cut and paste) the highlighted code below in to your Editor (I use the Spyder interface), you will find that Python returns solutions, within the Console, to each of the seven ODEs at the end of this program. You can also perform more standard differentiation and integration, not to mention production of top-notch 2D and 3D graphical plots, using similar code, but I hope that what I have written below is helpful to you to start with. I have checked that it works, but if you do have any problems, try refreshing the Kernel and then run the program again. Do let me know how you get on with it.

Kind regards,

Stephen

import numpy as np

import matplotlib.pyplot as plt

from sympy import init_printing

init_printing()

integrate(x)

from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols

from sympy.abc import x

f = Function('f')

from IPython.display import display

display(dsolve(Derivative(f(x), x) - f(x), f(x)))

display(dsolve(Derivative(f(x), x, x) + x*Derivative(f(x),x) + f(x), f(x)))

display(dsolve(Derivative(f(x), x, x) + Derivative(f(x),x) + f(x), f(x)))

display(dsolve(Derivative(f(x), x, x) + 5*Derivative(f(x),x) + f(x), f(x)))

display(dsolve(x*Derivative(f(x), x, x) + Derivative(f(x),x) + x*f(x), f(x)))

display(dsolve((x**2)*Derivative(f(x), x, x) + x*Derivative(f(x),x) + f(x), f(x)))

display(dsolve((x**2)*Derivative(f(x), x, x) + x*Derivative(f(x),x) + (x**2)*f(x), f(x)))