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I need to find the following: $$ -2\frac{\partial^2 Y_0}{\partial x\,\partial\zeta}-\frac{\partial Y_0}{\partial x}-xY_0 $$ given: $$ Y_0=A_0 (x)+B_0 (x)e^{-\zeta} $$

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If you intended to write partial derivatives, use $\partial$ ("\partial") instead of $\delta$. – Johnny Westerling Sep 29 '12 at 14:55
up vote 1 down vote accepted

Well, $\displaystyle\frac{\partial Y_0}{\partial x} = A_0'(x)+B_0'(x)e^{-\zeta}$,

then $\displaystyle\frac{\partial^2 Y_0}{\partial x\partial\zeta} = \frac{\partial}{\partial\zeta}\frac{\partial Y_0}{\partial x} = -B_0'(x)e^{-\zeta}$.

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