## Related questions with answers

Question

In the analysis of the bending of a uniformly loaded circular plate, the equation $w(r)$ of the deflection curve of the plate can be shown to satisfy the third-order differential equation

$\frac { d ^ { 3 } w } { d r ^ { 3 } } + \frac { 1 } { r } \frac { d ^ { 2 } w } { d r ^ { 2 } } - \frac { 1 } { r ^ { 2 } } \frac { d w } { d r } = \frac { q } { 2 D } r,$

where $q$ and $D$ are constants. Here $r$ is the radial distance from a point on the circular plate to its center. (a) Find the general solution of the equation.

Solution

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1 of 6We need to solve the following Cauchy-Euler DE

$\dfrac{d^3w}{dr^3} + \dfrac{1}{r} \dfrac{d^2w}{dr^2} - \dfrac{1}{r^2} \dfrac{dw}{dr} = \dfrac{q}{2D} r.$

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