My Math Forum Show that an equation satisfies a differential equation

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 February 24th, 2013, 10:30 AM #1 Member   Joined: Aug 2012 Posts: 88 Thanks: 0 Show that an equation satisfies a differential equation Show that $y= e^{x} + e^{-\frac{x}{2}}$ satisfies $2y'' - y' - y = 0$ So $y' = e^{x} - \frac{1}{2}e^{-\frac{x}{2}}$ and $y'' = e^{x} + \frac{1}{4}e^{-\frac{x}{2}}$ Then: $2(e^{x} + \frac{1}{4}e^{-\frac{x}{2}}) - (e^{x} - \frac{1}{2}e^{-\frac{x}{2}}) - (e^{x} + e^{-\frac{x}{2}}) = 0 \\\\ -e^{-\frac{x}{2}} = 0$ Never mind, I figured out my error... it was a sign mistake.

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