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Differential Equations Lecture Work Solutions 276

Differential Equations Lecture Work Solutions 276 - = − 1...

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1a. u ( x, t ) = F ( x ct ) Use the chain rule: ∂ u ∂ t = c dF ( x ct ) d ( x ct ) at t = 0 ∂ u ∂ t = c dF ( x ) dx 1b. ∂ u ∂ x = dF ( x ct ) d ( x ct ) · 1 at x = 0 ∂ u ∂ x = dF ( ct ) d ( ct
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Unformatted text preview: ) = − 1 c dF ( − ct ) dt = F ( − ct ) ↑ diferentiation with respect to argument 276...
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