This isn't a homework problem so hopefully this section is fine.(adsbygoogle = window.adsbygoogle || []).push({});

I came across something that's bothering me while reviewing PDEs.

Take something like: [tex]u_{x}(x,t) = 1.[/tex] which has the general solution: [tex]u(x,t) = c_{1}(t) + x.[/tex] Wolfram says this is linear but if I take a different solution: [tex]v(x,t) = c_{2}(t) + x[/tex] and add it to u it's not also a solution: [tex]u + v = c_{1}(t) + c_{2}(t) + 2x\\ (u + v)_{x} = 2 \neq 1[/tex]

I must be missing something really simple here.

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# Linearity of PDE

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