Integrale si ecuatii diferentiale.pdf - Profs.info.uaic.ro
Integrale si ecuatii diferentiale.pdf - Profs.info.uaic.ro
Integrale si ecuatii diferentiale.pdf - Profs.info.uaic.ro
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2.5. ECUAŢII CU DERIVATE PARŢIALE DE ORDINUL I 492.29 x 1∂u∂x 1+ . . . + x n∂u∂x n= ku.Determinaţi suprafeţele z = z(x, y) care includ curbele indicate:2.30 x ∂z∂x − y ∂z∂y= z, (Γ) : x = y, z = x22.31 x 2 ∂z ∂z− xy∂x ∂y + y2 = 0, (Γ) : y = 1, z = x 22.32 xy 2 ∂z∂x + x2 y ∂z∂y = z(x2 + y 2 ), (Γ) : y = 1, x 2 + z 2 = 12.33 (x − y) ∂z∂x − y ∂z∂y2.34 (1 + √ z − x − y) ∂z∂x + ∂z∂y2.35 (cy − bz) ∂z + (az − cx)∂z∂x ∂y2.36 (y − z) ∂z − (y − 1)∂z∂x ∂y= z, (Γ) : x = y, z = x2= 2, (Γ) : x = y, z = 0= bx − ay, a, b, c ∈ R (Γ) : x = y = z= z − 1, (Γ) : x = 1, z = y22.37 (y 2 + z 2 − x 2 ) ∂z ∂z− 2xy∂x ∂y = −2xz, (Γ) : x = 1, y2 + z 2 = 2.Rezolvaţi p<strong>ro</strong>blemele Cauchy:2.38 x ∂z ∂z+ 2y∂x ∂y2.39 (x + y) ∂z + (x − y)∂z∂x ∂y= 0, z(1, y) = 1 + y2.40 √ x ∂u∂x + √ y ∂u∂y + √ z ∂u∂z2.41 x ∂z∂x + y ∂z∂y = z, z| {x 2 +y 2 =1} = x= 0, z(x, 0) = −x2= 0, u(x, y, 1) = x − y2.42 x ∂u∂x − y ∂u∂y + z ∂u∂z = x2 , u(1, y, z) = y 2 − z