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4 1. INTRODUCTION
5. Heat (or diffusion) equation
ut − Δu = 0.
6. Schr¨odinger’s equation
iut + Δu = 0.
7. Kolmogorov’s equation
ut −
n
i,j=1
aijuxixj
+
n
i=1
biuxi
= 0.
8. Fokker–Planck equation
ut −
n
i,j=1
(aiju)xixj
−
n
i=1
(biu)xi
= 0.
9. Wave equation
utt − Δu = 0.
10. Klein–Gordon equation
utt − Δu +
m2u
= 0.
11. Telegraph equation
utt + 2dut − uxx = 0.
12. General wave equation
utt −
n
i,j=1
aijuxixj
+
n
i=1
biuxi
= 0.
13. Airy’s equation
ut + uxxx = 0.
14. Beam equation
utt + uxxxx = 0.

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