Solve equation:

$\displaystyle -u_{xxxx}(x,t)=\lambda u(x,t)$, $\displaystyle 0<x<L$

^{$\displaystyle u(0)=u(L)=0 $, $\displaystyle u_{xx}(0)=u_{xx}(L)=0$ }

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- Jun 20th 2013, 11:10 PMpinkfrogbeam equation
Solve equation:

$\displaystyle -u_{xxxx}(x,t)=\lambda u(x,t)$, $\displaystyle 0<x<L$

^{$\displaystyle u(0)=u(L)=0 $, $\displaystyle u_{xx}(0)=u_{xx}(L)=0$ } - Jun 22nd 2013, 02:56 PMmopen80Re: beam equation
Hi ,

Using Matlab Dsolve function i get that u=0; no beam deflection! - Jul 6th 2013, 01:18 PMHallsofIvyRe: beam equation
You don't really need "DSolve". The general solution to any linear homogeneous differential equation is a linear combination of the elementary solutions. The conditions that all values be 0 then must give u identically equal to 0 as the solution. (And it should be easy to see that u= 0 for all x

**does**satisfy the equation and additional conditions.)