Capitolul 1 Ecuatii diferentiale de ordinul ˆıntâi rezolvabile prin ...

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174 CAPITOLUL 5 Exercit¸ii: 1. Rezolvat¸i urmǎtoarele ecuat¸ii cu derivate part¸iale de ordinul întâi cvasiliniare: a) ∂u ∂x · (1 + √ u − x − y) + ∂u ∂y b) n i=1 xi · ∂u ∂xi = 2 R: γ(u − 2y, y + 2 √ u − x − y) = 0 R: γ = m · u x1 xn , x2 xn , . . ., xn−1 xn c) xy · ∂u ∂x − y2 · ∂u ∂y + x(1 + x2 ) = 0 R: γ xy u + x2 2 d) 2y4 · ∂u ∂u − xy · ∂x ∂y = x√u2 + 1 , u xm = 0 n x2 + , xy = 0 4 R: γ x 2 + y 4 , y u + √ u 2 + 1 = 0 2. Rezolvat¸i urmǎtoarele probleme Cauchy: a) ∂u ∂u − ∂x ∂y b) xy · ∂u ∂x − y2 · ∂u ∂y y − x = , u(1, y) = y2 u R: u 2 (x, y, z) = (x + y − 1) 4 + 2xy − 2(x + y − 1) = x, u(1, y) = 3 2y R: u(x, y) = x2 + 2 2xy
Ecuat¸ii cu derivate part¸iale de ordinul întâi cvasiliniare 175 c) u · ∂u ∂x + (u2 − x 2 ) · ∂u ∂y + x = 0, u(x, x2 ) = 2x R: y 2 + u 2 (x, y) = 5 (x · u(x, y) − y)
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Capitolul 1 Ecuat¸ii diferent¸ial
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Problema primitivei. Ecuat¸ii dife
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Problema primitivei. Ecuat¸ii dife
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Ecuat¸ii diferent¸iale autonome
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Ecuat¸ii diferent¸iale autonome
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Ecuat¸ii diferent¸iale cu variabi
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Ecuat¸ii omogene în sens Euler 17
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Ecuat¸ii omogene generalizate 19 1
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Ecuat¸ii diferent¸iale liniare de
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Ecuat¸ia diferent¸ialǎ a lui Ber
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Ecuat¸ia diferent¸ialǎ a lui Ber
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Ecuat¸ia diferent¸ialǎ a lui Ric
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Ecuat¸ii cu diferent¸ialǎ total
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Ecuat¸ii cu diferent¸ialǎ total
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Calculul simbolic al solut¸iilor e
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Capitolul 2 Ecuat¸ii diferent¸ial
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Ecuat¸ii diferent¸iale de ordinul
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Reducerea ecuat¸iei diferent¸iale
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Capitolul 3 Sisteme de ecuat¸ii di
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Sisteme de ecuat¸ii diferent¸iale
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Reducerea ecuat¸iilor diferent¸ia
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Calculul simbolic al solut¸iilor s
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Teoreme de existent¸ǎ ¸si unicit
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Proprietǎt¸i calitative ale solut
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Page 123 and 124: Proprietǎt¸i calitative ale solut
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Page 141 and 142: Metode numerice 141 > end if; > end
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Page 147 and 148: Metode numerice 147 Figura 19 > wit
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Page 155 and 156: Integrale prime 155 Întrucât (t0,
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Problema Cauchy-Dirichlet pentru ec
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Calculul simbolic ¸si numeric pent
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Bibliografie [1] V.I. Arnold, Ecuat
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BIBLIOGRAFIE 281 [26] M.Stoka, Cule
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