Solve uх (у — 2и) + и, у %3D —2х— у, и(х, 1) 3 х + 1. i.e. find an explicit solution for u = :(x, y) subject to u = x + 1 when y = 1. u(x, y) =|

Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: d) Solve: y"+y"-5y' + 3y = 0

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Q: Find u x v, v x u, and v x v. u = 5i + 9k v = 2i + 9j – 4k. (a) U X V (b) (c) v x v

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Q: es of the form rar, s = x+by, wher comes u, = u. e solution of u, -uy = u with u(0, y

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Q: Solve:

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Q: Solve for (x, y, z): 2x-2y+z=10 x+y-4z = - 17 3x-y + 2z = 13 O (4, -2, 1) O (1, -2, 4) O (2, 4, -1)

A: We have,  2x-2y+z=10 , x + y - 4z = -17 , 3x - y +2z = 13

Q: Find the linit. NOTE: Enter an exact limit if it erists. If the limit does not erist, indicate that…

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Q: u" - 16u = 0

A: Given the differential equation is u" - 16u = 0. Here the auxiliary equation is m2 - 16 = 0

Q: Find the general solution of x²y" + 10xy + 8y = x² Use the variation of parameters.

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Q: Find two linearly independent solutions of y" + 1xy = 0 of the form Y₁ = 1+ a3x³ + α6x6 +.. Y₂ = x +…

A: The given problem is to find the coefficients of the 2 linearly independent solutions for the given…

Q: a) x2y"+ xy' +(x2- 25)y = 0 b) (1 - x2) y" - 2xy' + 42y = 0 %3D %3D

A: a. Bessel ordinary differential equation has the form of x2y''+xy'+x2-v2y=0. Now, Rewriting the…

Q: y" + 4y + 4y = e-2x x²

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Q: Reduce the equation yzxx + (x + y)2xy + XZyy = 0 to a canonical form and solve it.

A: The characteristics integrals:

Q: Find x and y given that (x+yi)/2+i = (1-i)/2+3i

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Q: Determine Cif u=v=0 (20 — 5и + 3)dv — (20 + 4и — 6)du %3D 0

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Q: Verify that y, = e2x and y2 = e5×are solutions of у" - 7у' + 10у %3D 0

A: We have to verify that the functions y1=e2x and y2=e5x are solutions to the given differential…

Q: SOLVE THE FIRST ORDER DE. (x³ + y*)dx + 8y³xdy = 0 when x = 4, y = 2

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Q: Find u x v, v x u, and v x v. u = 5i + 9k v = 6i + 9j - 5k. (a) u xv (b) vxu (c) vxv

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Q: y - y = x C. d. у +у — 7у — у + бу %3D 0 (4) y

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Q: 2. (LI-2) Consider the equation r2y" - xy + y = 0. It is given that y₁ = z is one solution to this…

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Q: 9x-y+z=3 10x-y+z=8 Find (x,y,z)

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Q: Solve zx+zzy= 2x, z(0, y) = y

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Q: 1. х2у" — 20у%3D 0

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Q: Consider the equation x² + y³ + zª − 8xyz = z². Find z point (1,1,1). at the

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Q: What is the general solution of the   uyy=4x2u+yx2ex equation.

A: As per the question we are given a nonhomogeneous partial differential equation as : uyy = 4x2u +…

Q: Eliminate the arbitrary constants on the given equation: y= Ae" + Bre 2y +y=0 O y =-y" + 2g

A: The given equation is y=Aex+Bxex. We have to eliminate the arbitrary constants.

Q: Find two linearly independent solutions of 2x²y" - xy + (-4x + 1)y=0, x > 0 of the form y₁ = x¹(1+…

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Q: 3.a) Eliminate the Arbitrary Constants in the equation: y = C1sin(2x + C2) y" + 4y = 0 у' — 4у%3D0 O…

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Q: 5) x2. dx = x² + 3xy + y², (c) dr = 2 = 3v, + 3x' (d) (1 - y)' + By - 5x = 0.

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Q: Find the general solution for y"" + 2y" + 2y' = 0

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Q: y₁=1+a3x³ + arº +... Y₂ = x + b₁x¹ + b₁x² + ... Enter the first few coefficients: a3 = a6 = b₁ b7 )…

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Q: Uz + xuy = x²y, u ( x, 2x + = 5x

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Q: ) Find the mass of the solid E that lies above the cone v3z = Vx² + y² and the spheres x2 + y² + z²…

A: Given:   The Solid lies above the cone 3z=x2+y2 and between the sphere x2+y2+z2=1 and  x2+y2+z2=4…