Newton had a strange way to write about derivatives. His Method of Fluxions solved ordinary differential equations. Also the question whether Newton used partial differential equations already is under dispute. Cajori argues that Newton did not use partial differential equations.

*"The conclusion is firmly established that neither Newton nor Leibniz in their published writings ever wrote down a partial differential equation and proceeded to solve it."*

Of course this assertion of Cajori assumes (as we do in our courses) that an ordinary differential equation is not a partial differential equation even so one could take the point of view that ordinary differential equations form a subset of partial differential equations, equations which only use the derivative with respect to one variable.