My current understanding of differential equations is extremely shaky, and my vocabulary is probably very incorrect, but I'm curious about something I've recently seen in some Khan Academy videos (specifically this one) and in other situations with differential equations. It seems that the following is true:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d}{dx} \psi (x, y) = \frac{∂\psi}{∂x}\frac{dx}{dx} + \frac{∂\psi}{∂y}\frac{dy}{dx} [/tex]

Why is this? The video on Khan Academy shows a "proof" by which he assumes ##\psi## can be represented by a sum of products of functions of x and y (##\psi = f_1(x)g_1(y) + ... + f_n(x)g_n(y)##). What is the basis of this "proof"? Why could some function of x and y, psi, be displayed as products of separate functions of x or y?

I feel as though following the flow of videos on Khan Academy isn't explaining differential equations well-enough for me. Can anyone here recommend where else I might look to learn about differential equations?

Thanks for any help!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Why is differential equation equal to sum of partials?

Loading...

Similar Threads for differential equation equal |
---|

A Vector differential equation |

I Linear differential equation |

B What's the difference between 1000e^0.05t and 1000*1.05^t? |

Confusion about series solutions to differential equations |

A Runge Kutta finite difference of differential equations |

**Physics Forums | Science Articles, Homework Help, Discussion**