Differential Equations for Engineers and Scientists by C. G. Lambe & C. J. Tranter

Author:C. G. Lambe & C. J. Tranter [Lambe, C. G.]
Language: eng
Format: epub, mobi
Publisher: Dover Publications

in the form u = f(x) sin nt such that ∂ u/∂t = k (constant) when x = 0 and when t = 0 and also such that ∂u/∂x = 0 when x = 0 for all t.

8. Find a solution of the equation

such that when y = nπ/α (where n is an integer and a is a constant), V = 0 and ∂V/∂y = e2ax.

9. Assuming that u = r−1F(r) cos (ωt + α) is a solution of the partial differential equation

where ω, α and c are constants and F(r) is a function of r only, obtain the ordinary differential equation satisfied by F(r) and give the general solution for F(r). Given that, for all values of t, (i) u is finite at r = 0, (ii) ∂u/∂r = 0 at r = a and that u is not identically zero, prove that (ωa/c)− β must satisfy the equation β = tan β. (L.U.)

10. If u satisfies the differential equation

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