In this video we learn how to form a partial differential equation by eliminating arbitrary constants with the help of three examples.
If there are 2 arbitrary constants in a relation involving three variables x,y, and z, we need 3 equations to eliminate the 2 arbitrary constants. One equation will be the given relation. The other two equations we will obtain by taking first order partial derivative of the given relation with respect to x and y, and therefore we will obtain a first order PDE.
If there are 3 arbitrary constant in a relation involving three variables x, y, z, we need 4 equations.The fourth equation we will obtain by producing a 2nd order mixed derivative.
To learn more watch the video till end.
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