Let d = gcd(a, b). If (xo, yo) is a solution of the linear Diophantince equation ax + by = c, %3D which of the following is also a solution?

Q: Solve the general solution of the given DE: dyldx = (2y/x) + (3x/2y).* %3D

A: Suppose any linear differential equation can be written in the form of  dydx=fyx then it is a…

Q: Obtain the homogeneous linear equation satisfied by the following given function 1. y =x2 (e5x + 4)

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Under what conditions is yb+6c perpendicular to a? What does this say about the coefficients of b…

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Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex² False True O

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Q: Show that the equation dy + 2k possesses solutions of the form 00 -kt E C, e cos (C, x+ E,) cos…

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Q: If y1, Y2 · Y3 are solutions to y'"+p(x) y' +q(x) y = 0, then {y1, Y2, Y3} is Linearly dependent.…

A: The given differential equation have y1,y2 , y3 as solution .  So, we know that linear combination…

Q: If y, and y₂ are linearly independent solutions of ty" + 3y' + tety = 0 and if W(y₁, y₂)(1) = 6,…

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Q: Show that the equation dy + 2k possesses solutions of the form E c, e cos (a,x+&,) cos (w,t+ 8,)…

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Q: The linear Diophantine equation ах + бу — С = c has a solution if, and only if,

A: The linear diophantine equation is in the form, ax+by=c,

Q: If y1, Y2 Y3 are solutions to y"+p(x) y' +q(x) y =0, then {y,, Y2 • Y3} is Linearly dependent.…

A: We have to tell about given statement.

Q: a) Solve the following linear equation by Cramar's - y + 2z = -4 Bx + y – 4z = –6

A: In this question, the concept of the Cramer rule is applied. Cramer Rule Cramer's rule is an…

Q: Determine the general solutions of the following non homogenous linear equations. 1. (D2 + D)y = sin…

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Q: Q1: Apply Gauss Seidel method to solve the following linear equations, starting from 1,1,15…

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Q: Solve the following Euler-Cauchy type equation: 1 (2²D² + 3xD+ 1)y %3D (1 – x)²'

A: The given ODE is given as: x2D2+3xD+1y=11−x2

Q: Use Gauss- Jordan to solve the values of x,y and z for this problem: 2x – y+z =-3 x+y-z = 6 3x - y-…

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Q: ,solve x′= Ax by determining n linearly independent solutions of the form x(t)=eAtv.

A: To Determine: solve x′= Ax by determining n linearly independent solutions of the form x(t)=eAtv.…

Q: Determine the general solutions of the following 5. (D3 – D2+ D– 1) y = 4 sin x non homogenous…

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Q: Find the solution of y'(x) -ay(x) = 0

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: Solve the following Euler-Cauchy type equation: 1 (x² D² + 3xD+ 1)y = - 3xD+ 1)y = (1 – x)² ' d…

A: Given equation is, x2D2+3xD+1y=1(1-x)2 Take, (x2D2+3xD+1)y=0 Then assume, y=xn,…

Q: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…

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Q: If y, and y₂ are linearly independent solutions of ty" + 2y + tey = 0 and if W(₁,₂)(1) = 5, find…

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Q: Let a ∈ R and find the solution to y'(t) - a y(t) = 0.

A: The given differential equation is dydt-ay=0 , a∈R.we will slove this by the method of  separartion…

Q: Show that a linear equation dy a(x) + b(x)y = c(x) %3D dx is exactif a' (x) = b(x).

A: A differential equation of type  P(x,y)dx + Q(x,y)dy =0 will be an exact differential equation if…

Q: Find the general solution of the following homogeneous linear equations: A. (D3+8)y=0

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Q: If y, and y, are linearly independent solutions of ty" + 3y' + tey = 0 and if W(y,, y2)(1) = 6, find…

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Q: Show that the equation Əy 2 a3y + 2k possesses solutions of the form 00 -kt E C,e cos (C, x+ E,) cos…

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Q: If yi = 1, Y2 = In a are two linearly indepen- dent solutions of ry"+y' = 0, then the partic- ular…

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Q: If y = x2 is one solution of x2y''+2xy'-6y=0 and the other linearly independent solution.

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Q: (a) Solve the following linear equation by Cramar's rule:- x- y + 2z = –-4 3x + y – 4z = -6 2x + 3y…

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Q: Observe that y = x is a particular solution of the equation %3D 2x²y" + xy' – y = 0 and find the…

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Q: Let d = gcd(a, b). If (xo, Yo) is a solution of the linear Diophantince equation ax + by = c, which…

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Q: dy + ydx %3D = 3x²y?dx,

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Q: Ify, and y, are linearly independent solutions of y" + 2y + (3 + 1)y = 0 and if W(y1, y2)(1) = 2.…

A: I am solving this in step 2

Q: Find the solution of the Euler-Cauchy equation x?y" + 0.6xy' + 16.04y = 0.

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Q: If y, and y, are linearly independent solutions of ty" + 2y' + te" y = 0 and if W(y1, y2)(1) = 2,…

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Q: (a) Solve the following linear equation by Cramar's rule:- x - y + 2z = -4 3x + y - 4z = -6 2х +…

A: We have given equation x-y+2z=-4 3x+y-4z =-6 2x+3y-4z=4 Matrix representation of equation  AX=B…

Q: Solve the given LDE using the method of UNDETERMINED COEFFCIENTS.  1. y''' - y' = 4e^(-x) +…

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Q: Assume that y1(t) = e^2t and y2(t) = e^−2t are solutions, show that these two solutions are linearly…

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Q: 1. Find the order and degree of each DE, and state whether it is linear or nonlinear and why? a.…

A: The solution is given below

Q: Given that y, =t2 is a solution to the DE ty" - 3ty' + 4y = 0 on (0, o0), use reducti econd…

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Q: x + 2y + z – t = 5 입+y+ 2z+ 2t = 8 4x + 4y + 3z + 4t = 22 1 x + -z+t = 3

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Q: Determine if the given DE is a solution of y" + 2y'+y x y(x) = 1

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Q: Show that ysecc) is a solution to i y"-2tanG)y 0, and use reduction of order to find a Second,…

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Q: хdy — (у+2х"2)dx %3D (у+2x^2)dх %3D о

A: Given: xdy-y+2x2dx=0

Q: A third-order Euler equation is one of the form ax°y"' + bx-y" + cxy' + ky = 0, where a, b, c, and k…

A: Givenax3y"' +bx2y" +cxy' +ky=0 ----1after subsitution V =lnx Transformed into constant coefficient a…

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y(-)= 3x²y² becomes A none…

A: We have to write the differential equation in terms of dz/dx.

Q: (a) If b – 4ac = 0 and y1 = em solves ay" + by' + cy = 0, use reduction of order to get a linearly…

A: A set of vectors is said to be linearly dependent if there is a nontrivial linear combination of the…

Q: 21/ solve one of the following Linear system: dx 1. - y = t? dt 2+ 4x = 1 dt

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Show that the equation dy + 2k possesses solutions of the form 00 -kt E C, e cos (C, x+ E,) cos…

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Q: If the functions y, and y2 are linearly independent solutions of y" +p(t)y +q()y = 0, Czy2 are also…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.