Definition:Partial Differential Equation/Historical Note

Historical Note on Partial Differential Equation
The first partial differential equation to be recognised as such was the one which defines the form of a vibrating string.

It was discussed by and  in $1747$.

completed the solution of that equation.

Between $1772$ and $1785$ he also addressed the partial differential equation of the first order.

He established the general solution of the linear equation, and classified the various kinds of non-linear equation.

Work is still being done on these equations.