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The one dimensional wave equation describes how waves of speed c propogate along a taught string. It is given by the formula 2u(x, t) = c²– da?u(x, t). ςu (r, t). This is a partial differential equation. In MATH2, solve ordinary differential equations. However, using the multivariable chain rule, we’ll show that this problem is indeed tractable we’ve only learned how to a) By introducing variables n = x – ct, a =x + ct, show that the wave equation becomes da = 0 b) Show that u = F(@) + G(ŋ) is a solution for any two functions F and G.

The one dimensional wave equation describes how waves of speed c propogate along a taught string. It is given by the formula 2u(x, t) = c²– da?u(x, t). ςu (r, t). This is a partial differential equation. In MATH2, solve ordinary differential equations. However, using the multivariable chain rule, we’ll show that this problem is indeed tractable we’ve only learned how to a) By introducing variables n = x – ct, a =x + ct, show that the wave equation becomes da = 0 b) Show that u = F(@) + G(ŋ) is a solution for any two functions F and G.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. The one dimensional wave equation describes how waves of speed c propogate along a taught string. It is given by the formula Ət2u(x, t) = c²- da2 u(x, t). This is a partial differential equation. In MATH , we’ve only learned how to solve ordinary differential equations. However, using the multivariable chain rule, we’ll show that this problem is indeed tractable a) By introducing variablesn= x – ct, a = x + ct, show that the wave equation becomes da = 0 n- b) Show that u = F(a) + G(n) is a solution for any two functions F and G.
Transcribed Image Text:4. The one dimensional wave equation describes how waves of speed c propogate along a taught string. It is given by the formula Ət2u(x, t) = c²- da2 u(x, t). This is a partial differential equation. In MATH , we’ve only learned how to solve ordinary differential equations. However, using the multivariable chain rule, we’ll show that this problem is indeed tractable a) By introducing variablesn= x – ct, a = x + ct, show that the wave equation becomes da = 0 n- b) Show that u = F(a) + G(n) is a solution for any two functions F and G.
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