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. 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> :

then the derivatives of y in the ordinary equation may be [[partial derivative]]s 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^2 y}{\partial x^2} = \frac{1}{c^2}\frac{\partial^2 y}{\partial t^2}</math>

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

==References==

==References==

     <small><references/></small>

     {{Reflist}}

==See also==

==See also==

*[[Laplace transform]]

*[[Laplace transform]]

*[[Separation of variables]]

*[[Separation of variables]]

[[category:calculus]]

[[Category:Calculus]]

[[Category:Differential Equations]]

[[Category:Differential Equations]]