#### dRic2

Gold Member

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Can anyone provide some simple references where I can find at least an intuition regarding what is stated by the author.It is in the general theory of differential equations that the right-hand side of

$$y''''(x) = \rho (x)$$

can be prescribed arbitrary only if the corresponding homogeneous differential equation has no solution except the trivial solution ##y=0##. In all the previous cases the boundary conditions were such that the differential equation

$$y''''(x) = 0$$

had no solution under the given boundary conditions. Here, however, two such independent solution exist, namely

$$y = 1$$

$$y = x$$

In such case our boundary value problem is not solvable unless ##\rho(x)## is "orthogonal" to the homogeneous solutions - i.e.

$$\int_0^l \rho(x)dx = 0$$

$$\int_0^l \rho(x)xdx = 0$$

Thanks,

Ric