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The fascinating story of direction fields

The great thing about direction fields of differential equations is that they resemble looking at a painting through a hole in a needle. You can see each portion of the painting very well, you can see the colors, maybe the texture; you can even connect the nearby frames into one piece, but you can never get the final complete impression of what the painting looks like.

Direction field of a function y’ = y + t drawn by dfield7.