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Exact Solutions > Linear Partial Differential Equations > Second-Order Hyperbolic Partial Differential Equations PDF version of this page

## 2. Linear Hyperbolic Equations

1. wtt = a2wxx.    Wave equation (linear wave equation).
2. wtt = a2wxx + Φ(x, t).    Nonhomogeneous wave equation.
3. wtt = a2wxxbw.    Klein-Gordon equation.
4. wtt = a2wxxbw + Φ(x, t).    Nonhomogeneous Klein-Gordon equation.
5. wtt = a2(wrr + r−1wr) + Φ(r, t).    Nonhomogeneous wave equation with axial symmetry.
6. wtt = a2(wrr+2r−1wr) + Φ(r, t).    Nonhomogeneous wave equation with central symmetry.
7. wtt + kwt = a2wxx + bw.    Telegraph equation.

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