2c1. Derive d'Alembert's formula u(x, t) = ½ (ƒ (x − ct) + ƒ (x + ct)) + 1/4 fr+ctg(s)ds by determining thetwo arbitrary functions F and G in the general solution u(x, t) = F(x− ct)+G(x+ct) using the initialconditions u(x, 0) = f(x), ut(x, 0) = g(x), x € R.

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1. Derive d'Alembert's formula u(x, t) = ½ (ƒ (x − ct) + f (x + ct)) + f + g(s)ds by determining the x+ct 2c Jx-ct two arbitrary functions F and G in the general solution u(x, t) = F(x- ct) +G(x+ct) using the initial conditions u(x, 0) = f(x), u₁(x, 0) = g(x), x = R.

1. Derive d'Alembert's formula u(x, t) = ½ (ƒ (x − ct) + f (x + ct)) + f + g(s)ds by determining the x+ct 2c Jx-ct two arbitrary functions F and G in the general solution u(x, t) = F(x- ct) +G(x+ct) using the initial conditions u(x, 0) = f(x), u₁(x, 0) = g(x), x = R.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 2E

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Question

2c
1. Derive d'Alembert's formula u(x, t) = ½ (ƒ (x − ct) + ƒ (x + ct)) + 1/4 fr+ctg(s)ds by determining the
two arbitrary functions F and G in the general solution u(x, t) = F(x− ct)+G(x+ct) using the initial
conditions u(x, 0) = f(x), ut(x, 0) = g(x), x € R.

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