Exact Solutions > Linear Partial Differential Equations > Higher-Order Partial Differential Equations ## 5. Fourth-Order Partial Differential Equations-
*w*_{tt}+*a*^{2}*w*_{xxxx}= 0. Equation of transverse vibration of elastic rods. -
*w*_{tt}+*a*^{2}*w*_{xxxx}= Φ(*x*,*t*). Equation of transverse vibration of elastic rods (nonhomogeneous). -
ΔΔ
*w*= 0. Biharmonic equation. -
ΔΔ
*w*= Φ(*x*,*y*). Nonhomogeneous biharmonic equation.
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