Suppose we have a first order linear PDE of the form:(adsbygoogle = window.adsbygoogle || []).push({});

a(x,y) u_{x}+ b(x,y) u_{y}= 0

Thendy/dx = b(x,y) / a(x,y)[assumption: a(x,y) is not zero]

The characteristic equation for the PDE is

b(x,y) dx - a(x,y) dy=0

d[F(x,y)]=0

"F(x,y)=constant" are characteristic curves

Therefore, the general solution to the PDE is u(x,y)=f[F(x,y)] where f is an arbitrary function.

===========================================

I don't understand the parts in red.

1) Why would dy/dx = b(x,y) / a(x,y) ? This doesn't seem obvious to me at all...how can we derive (or prove) it?

2) Also, what is the meaning of the equation d[F(x,y)]=0?

Thanks for explaining!

**Physics Forums - The Fusion of Science and Community**

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

# First order linear PDE

Loading...

Similar Threads - order linear | Date |
---|---|

A Solve a non-linear ODE of third order | Feb 20, 2018 |

A Solving linear 2nd order IVP non-constant coefficient | Jan 10, 2018 |

I Classification of First Order Linear Partial Differential Eq | Jan 2, 2018 |

I Question about second order linear differential equations | Aug 21, 2017 |

B First Order Non-Linear ODE (what method to use?) | Feb 14, 2017 |

**Physics Forums - The Fusion of Science and Community**