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3blue1brown has in fact written his own software to do these kinds of animations. It's called manim and it's open source on Github ->https://github.com/3b1b/manim
There is also a community maintained version ->https://github.com/ManimCommunity/manim/
Other approaches to do these kinds of animation would be to plot the graphs and equations in software like Desmos or GeoGebra and edit them together in a video editor. Alternatively, you could create it like you would create motion graphics with Adobe Illustrator + After Effects (or similar software).