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Mathematik-Online problems:

Problem 110: Solution of a Differential Equation

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Given the function

$\displaystyle u(x)=a{\rm {e}}^{2x}+b\,{\rm {e}}^x(\sin x+\cos x), \qquad a, b\in\mathbb{R}. $

Show that $ u$ is solution of the differential equation $ u'''-4u''+6u'-4u=0$, and determine $ a$ and $ b$ so that $ u(0)=0$ and $ u'(\frac{\pi}{2})={\rm {e}}^\pi$.

(Authors: Apprich/Höfert)

Solution:

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  automatisch erstellt am 23.  8. 2005