If x, x is a basis of solutions of r'y" + ary'+ by = 0, %3D then a = (A) -2 (B) 2 (C) -3 (D) 3 (E) None

Q: Cansider h(x)= Ilx? -6x = l|x? calculate Ha) 6 .x T1 3 (22r – 6) A) In(3)- 11 (22.r – 6)3** - (11z²…

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Q: Assume that the vectors sint cost X2= sint - cost , and X,= sint +cost sint -cost 0. sint +cost are…

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Q: 1. The vector X = k is a solution of x - (: -)x-G) 8, X' 2 for k = Enter only the value of k.

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Q: Solutions to second-order Cauchy-Euler equations with repeated roots of the characteristic equation…

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Q: function fo) = 7X1+10x10x3_4 Qn Antiderivative of fo) is F(x) = Axn+ Bxm, CxP+Dx: A= 710 %3D where…

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Q: Explain particular solution of the forced system                     x'' = Ax + F0 cos wt

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Q: Consider Diagonalize A, that is, find D and X auch that A = XDX-¹. Find the general solution to the…

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Q: Find two linearly independent solutions of 2x²y" - xy' + (−3x + 1)y = 0, x > 0 = x¹¹ (1 + α₁x + a₂x²…

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Q: Verify the orthogonality condition of each of the equations y" - 2xy' - 2ny = 0 11 ( where n is a…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Verify that the vector X, is a particular solution of the given nonhomogeneous linear system. 2 1 X'…

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Q: , Find two linearly independent solutions of 2a²y" – xy' + (2x +1)y = 0, x > 0 of the form Y1 = r"…

A: (Note: Please scroll to the last step for the final answer.) Given equation is 2x2y''−xy'+2x+1y=0…

Q: y = [ 0 1] (2x2 matrix) + [-1 0] d/dx y [1] (1x2 matrix) y (0) [1] [1] %3D [2]

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Q: (1x30'+ 3xD+1)y:о, усідів, у'(1)-о утобу'+0.09у= y (0) = 2.2, y' (0) = 0.14 -0.3x -o-3x e хе

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Q: Write the system y1 = -y1+2 cos(r)y3 + e 2 = xy1 - 10y2 + e" y3 +20 sin(x) Y3 = e2" y2 – a²y3 %3D…

A: The matrix form of given system of differential equations as follows

Q: Write a'= -3x+y+ln(t), y'= t'a in matrix form as 18 31 and f(t) is 181 [*] -= P(1) [*] + f(t) where…

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Q: (5). If A, B and A+B are each non-singular and the products are conformable, prove that (a). A(A +…

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Q: Verify that the vector Xp is a particular solution of the given nonhomogeneous linear system. dx dt…

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Q: () - - (a + bt c+ dt) e *() -- () a (:) - (-) A d - c

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Q: Verify that the vector X is a solution of the given homogeneous system. -1 x-(-; X'= 1 -1 x - (-²)…

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Q: 2. Differential equation for the circuit is Lv"(t) + Rv'(t) + A v(t) = 0. R Voltage source L Let V…

A: The differential equation for the circuit is Lv''t+Rv't+1cvt=0             (I) Let V be the vector…

Q: Give the General Solution.  (d/dt)(vector(x)) = matrix(2,3,-3,2)vector(x)

A: Given that,  ddtx1x2=23-32x1x2 The corresponding linear equations are, x1'=2x1+3x2x2'=-3x1+2x2…

Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: 9. Find the general solution of (D² – 2D+ 1)y= 6e*. A) y= (c, +c,x)e* + 3e™* B) y= (c, +c,x+ 3x² )e*…

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Q: Explain the conditions for the origin a node of the system x' = Ax?

A: The system of the first order differential equations x'=Ax is homogeneous and the matrix A is an n×n…

Q: . 2x²y" + 3xy' - (x² + 1)y = 0

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: x'1 = 3x1 + x2 + 3x3, x'2 = x1 +5x2 + X3, x'3 = 3x1 +X2 + 3x3 What is the general solution in matrix…

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Q: please solve asap

A: The given system of differential equations is:X′(t)=[34​−2−1​]X(t);X(0)=[−22​] (a).Now the…

Q: 2-2)(25p) Find the general solution of the following linear system of equations using characteristic…

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Q: What are the A) r₁ = 0, B) r₁=0, C) r₁3, D) T₁ = -1, Fa 0 characteristic roots of a homogeneous LDE…

A: If characteristic roots are ri then solution is of the form ∑cierix and if roots are repeated then…

Q: Write y – 2j + 5ý + y = = | as an autonomous system of first-order equations.

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Q: 2.) Find a general set of solution vectors of x'1=-5x2 x'2=x1+3x2

A: To find the general solution of a system of linear differential equations, follow these steps: 1.…

Q: Show that the 3D system x' = Ax is conjugate to the system x' = -x where a < 0 and A is given by 1 A…

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Q: y "- 3y + 2y =0 0 1 O b. ***-(2,₂3). x-(2-1) --(-) 0 1 X' 3 2 21 +-(-3) X'= 0 a. O c. O d. x x

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

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Q: The equations æy? + 6xzcos(u) + ye" = 12 and æ³yz+ xe® • 24 are solved for u and v as functions of…

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Q: 3. (Section 17.6) Determine the upward flux of F = through the part of z = x2 + y2 below z = 2.

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Q: The equations xy2 + 6xzcos(u) + ye" = 12 and x³yz + xe" - 8u²v² = 24 are solved for u and v as…

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