Is this linear homogeneous, linear inhomogeneous etc...(adsbygoogle = window.adsbygoogle || []).push({});

[tex]u_{t}-u_{xx}+xu=0[/tex]

From that first one I get this

[tex]\frac{u_{t}-u_{xx}}{u}=-x[/tex]

which I'm not sure is linear.

Edit:

Similar questions involve the following equations:

[tex]iu_{t}-u_{xx}+\frac{u}{x}=0[/tex]

and

[tex]u_{x}+e^{y}u_{y}=0[/tex]

Another Edit:

I think I see the answer. I can rewrite the first equation like this:

[tex](u_{t}-u_{xx}+xu)(\frac{1}{x})=0(\frac{1}{x})[/tex]

and get a linear equation:

[tex]\frac{u_{t}}{x}-\frac{u_{xx}}{x}+u=0[/tex]

UGH... Another Edit..

I'm not sure which approach is correct, the first or the second...

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

Join Physics Forums Today!

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

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

# Homework Help: Linearity of Partial Differential Equations

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