Changes

<math>y = F(u,v)</math>

<math>y = F(u,v)</math>

then the derivatives of y in the ordinary equation may be [[partial derivative|partial derivatives]] with respect to either u or v. In that case, any differential equation that has partial derivatives is called a partial differential equation.

then the derivatives of y in the ordinary equation may be [[partial derivative|partial derivatives]] with respect to either u or v. In that case, any differential equation that has partial derivatives is called a partial differential equation. For example, the 1-dimensional [[wave equation]]<ref>Pain, H.J. ''The Physics of Vibrations and Waves'' 6th edition. Southern Gate, Chichester, West Sussex, England: John Wiley & Sons, 2005</ref> :

<math>\frac{\partial y}{\partial u} = k\frac{\partial^2 y}{\partial v^2}</math>

<math>\frac{\partial^2 y}{\partial x^2} = \frac{1}{c^2}\frac{\partial^2 y}{\partial t^2}</math>

Obviously, partial differential equations are much more complicated to solve.

Obviously, partial differential equations are much more complicated to solve.