Partial Differential Equations - QMplus

10 CHAPTER 1. INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS Example 1.2.6. Let U x= 2xsiny+ exy: Direct integration gives U(x;y) = x2 siny+ exy y + f(y): And nally two more examples which will be further elaborated during the course: Example 1.2.7. One can readily verify by direct computation that U(x;y) = sin(nx)sinh(ny) solves U xx+ U yy= 0 ... ................
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