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**dwsmith** $\displaystyle u_{xxxx}+yu_{xxy}=0$

$\displaystyle \varphi^{(4)}(x)\psi(y)+y\varphi''(x)\psi'(y)=0$

$\displaystyle \displaystyle\frac{\varphi^{(4)}(x)}{\varphi''(x)} =-\frac{y\psi'(y)}{\psi(y)}$

$\displaystyle \displaystyle\int\frac{\varphi^{(4)}(x)}{\varphi'' (x)}$ How is this integrated?

Which way is this integrate:

$\displaystyle \displaystyle -\int\frac{y\psi'(y)}{\psi(y)}$

$\displaystyle \displaystyle -y\int\frac{\psi'(y)}{\psi(y)}=-y\ln{|\psi(y)|}$

or

If the y isn't treated as a constant, how is integrated?

Thanks.