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$w_{xxxx}+4w_{xy}=2 \tan x $

Is the pde quasi-linear, semi-linear or fully non-linear ?

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1 Answer 1

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Your equation is linear. Indeed if $w_1$ and $w_2$ are solutions of the homogenous equation $$w_{xxxx} + w_{xy} = 0$$ then $w_1 + w_2$ is also solution.

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  • $\begingroup$ Can you generalize it for other questions pls ? Specially, I don't understand the questions including terms $w_{xy}$ $\endgroup$
    – HD239
    Mar 24, 2017 at 12:35
  • $\begingroup$ What questions ? $\endgroup$
    – Héhéhé
    Mar 24, 2017 at 12:37
  • $\begingroup$ $$w_{xxx} + 2w_{xy}+w_{yy} = sinx$$. how to show that it is linear, semi linear , quasi linear or non linear ? Could you explain pls ? $\endgroup$
    – HD239
    Mar 24, 2017 at 12:41
  • $\begingroup$ Your equation is linear. Go check math.stackexchange.com/a/389382/427673 $\endgroup$
    – Héhéhé
    Mar 24, 2017 at 12:43
  • $\begingroup$ I checked. But there is no terms $u_{xy} $ in the definition ? $\endgroup$
    – HD239
    Mar 24, 2017 at 13:00

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