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I am trying to understand the balance of units for this eqn

## \displaystyle \frac{d^2}{dx^2}(E(x)I(x) \frac{d^2 w(x)}{dx^2})+c_f(x)w(x)=q(x)##

where ##E## is the modulus of Elasticity, ##I## is the second moment of area, ##c_f## is the elastic foundation modulus, ##w## is deflection and ##q## is the distributed transverse load.

Based on the above I calculate the units to be

## \displaystyle \frac{d^2}{dx^2}[\frac{N}{m^2} m^4 \frac{d^2 m}{dx^2}]+\frac{N}{m^2} m=\frac{N}{m}##

gives

##\displaystyle {Nm^3} +\frac{N}{m}=\frac{N}{m}##

##LHS \ne RHS##....?

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# Euler Bernoulli Beam 4th order ODE -Balance of Units

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