(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello, I should probably know how to do this, but I am confused as to how to solve the following 4th order ODE:

[tex]\begin{align}

& EI \frac{\mathrm{d}^4 w}{\mathrm{d} x^4} = 0 \\

& w|_{x = 0} = 0 \quad ; \quad \frac{\mathrm{d} w}{\mathrm{d} x}\bigg|_{x = 0} = 0 \quad ; \quad

\frac{\mathrm{d}^2 w}{\mathrm{d} x^2}\bigg|_{x = L} = 0 \quad ; \quad -EI \frac{\mathrm{d}^3 w}{\mathrm{d} x^3}\bigg|_{x = L} = F\,

\end{align}

[/tex]

The well-known solution is:

[tex]w = \frac{F}{6 EI}(3 L x^2 - x^3)\,~.[/tex]

...but I don't know how to obtain it myself.

3. The attempt at a solution

Since all the roots of the characteristic equation would be 0, the solution should be:

w = c1*exp(0*x) + c2*exp(0*x) +...+c4*exp(0*x)

Then normally one would use the initial conditions to get the constants, but that gives sth like the following system:

c1+c2+c3+c4 = 0

0 = 0

0 = 0

0 = 0

haha

in fact, I am not sure how one could get an equation with powers of x solving the equation this way. I must be going about this wrong or making a very simple mistake somewhere...

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# Homework Help: Solution of 4th order ODE

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