Folks,

Could anyone check my attached work. Mathematica seems to output u(x,y)=-3+2x for the particular solution...

Thanks

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- May 5th 2011, 11:22 AMbugatti791st Order Semi Linear PDE xu_x+yu_y=u+3
Folks,

Could anyone check my attached work. Mathematica seems to output u(x,y)=-3+2x for the particular solution...

Thanks - May 5th 2011, 01:39 PMTheEmptySet
If we parametrize x and y we have

and

Then

Now if we take the derivative with respect to s we have

This gives the system of equations

Solving this gives

Now if we sub out

we get

- May 5th 2011, 01:49 PMJester
Here's your mistake

First let so . If then so so (your Mathematica and TheEmptySet's solution) - May 5th 2011, 11:45 PMbugatti79
Cheers Danny!

I like this alternative method, TheEmptySet. Thanks