# Thread: Basic Linear Partial Differential Equation

1. ## Basic Linear Partial Differential Equation

I understand that for a basic equation of this form, we just want to make it an ODE so it is baby stuff to solve. Not really sure what to do with 3u since the derivative/chain rule don't apply.

Thanks!

2. If $u_s = u_{x_1} {x_1}_s + u_{x_2} {x_2}_s + u_{x_3} {x_3}_s$

and with your chose of

${x_1}_s = x_1,\;\; {x_2}_s = 2x_2,\;\; {x_3}_s = 1$

gives via your PDE

$u_s = 3u$.