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- Find two linearly independent solutions of 2x²y" - xy + (−4x + 1)y = 0, x > 0 of the form Y₁ = x¹(1+ a₁x + a₂x² + aşx³ + ...) Y2 = : x*²(1+b₁x+b₂x² + b3x³ + ...) where T₁ > T2. Enter 71 = a1 = a2 = az = r2 = b₁ = b₂ = b3 Ints) Find two linearly independent solutions of 2x²y" - xy + (2x + 1)y=0, x > 0 of the form Y₁ = x¹(1+ a₁ + a₂c² + a3x³ + ...) Y₂ = x²(1 + b₁c + b₂x² + b3x³ + ...) where T1 T2. Enter T1 T2 a1 = a₂ = a3 = b₁ b₂ TE b3 N - || || || || =Solve for the orthogonal trasctories x* ( 3k-x) - ky2 = xy2
- Find two linearly independent solutions of 2x²y - xy +(-3x+1)y=0, x > 0 of the form = x¹(1+x+q₂x² + x² + ...) 3₂ = x¹(1 + b₂x + b₂x² + b₂x² + ...) where r > 7₂.Obtain 2 linearly independent solutions valid near the origin for x>0 2ху" + 5(1 — 2х)у — 5у 3 0.Find Duf at P. = f(x, y, z) = 6x³y³z³; P(2, -2, 2); u Duf = i i + 2 - 2 k
- Ify %3D (x + 1)(2х -), then y' will be A. (x + 1)(2 – V) + (2x -) В. (х+ 1) + (2х-v)(2 — Vx) 1 c. (x+1)(2- + (2x – v3) х+ 1) (2 + (2х — Vx) С. D. (x+1)(2– D. (x+ 1)(2 + [2х 2Vx/ 2VxThe equations xy² + 6xzcos(u) + ye" = 12 and x³yz + xe" - 8u²v² = 24 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v)=(,0). Find ()zy at P. Türkçe: xy² + 6xzcos(u) + ye" = 12 ve x³yz + xe" - 8u²v² = 24 denklemleri P noktası (x,y,z)=(1,1,1) ve (u, v) = (,0) civarında x,y ve z'nin fonksiyonu olmak üzere u ve v için çözümlü olsun. P'de ()zy 'yi hesaplayınız.) O-0,33 O -0,17 12,00 -0,50 64,00 -56,00 -30,00 O 0,83provide complete solution showing the W1, W2, U'1, U'2, U1, U2, y(x)
- The equations æy? + 2xzcos(u) + ye" = 4 and x³yz + xe" – 8u²v² = 24 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) = (풍,0). Find (),y at P. | du dz 12,y Türkçe: xy? + 2xzcos(u) + ye" = 4 ve x³yz + xe" – 8u?v² = 24 denklemleri P noktası (x,y,z)=(1,1,1) ve (u, v) = (4,0) civarında x,y ve z'nin fonksiyonu olmak üzere u ve v için çözümlü olsun. P'de (u)zy'yi hesaplayınız.) dz O 64,00 O 4,00 O -10,00 O -0,50 O -80,00 "GenQ4/ A/If x² (y - 4z) - y² (2x + 3z) + z²(3x - 4y) = xyz Find ZxFind ∂y/∂x1 and ∂y/x2 y = 2x13 − 11x12x2 + 3x22 y = 7x1 + 6x1x22 - px23 y = (2x1 + 3)(x2 - 2) y = (5x1 + 3)(x2 - 2) y = (2x1 - 3x2) / (x1 + x2) y = (x12 - 1) / (x1x2)