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- W3021085430 abstract "Publisher SummaryThis chapter discusses exact equations. The concept is applicable to quasi-linear partial differential equations, and yields an exact solution. Some quasi-linear partial differential equations can be integrated directly. The procedure considers the quasi-linear partial differential equation M(x, y, u)ux = N(x, y, u)uy. If this equation satisfies the exactness condition Mx = Ny, then an implicit solution to M(x, y, u)ux = N(x, y, u)uy will be given by Φ(x, y, u) = 0, where M = Φy, N = Φx. To determine the function Φ, the equation M = Φy is integrated to obtain Φ = ∫Mdy + g(x, u). Using N = Φx gives ∫Mxdy + gx(x, u) = N." @default.
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- W3021085430 date "1992-01-01" @default.
- W3021085430 modified "2023-09-27" @default.
- W3021085430 title "Exact Equations" @default.
- W3021085430 doi "https://doi.org/10.1016/b978-0-12-784391-9.50105-6" @default.
- W3021085430 hasPublicationYear "1992" @default.
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