Use the method of variation of parameters to find the general solution of the following systems: 16. 3x1 – x2 – 5e2t x1 + x2 17. X1 – 6x2 4x1 + x2 - 2 cos 2t

Q: Sx+y= 1 (2х +у %3D 3 3. Solve the system for vectors in the field Z,.

A: Given: The given system is x+y=12x+y=3

Q: Find all solutions to (2cos x+ V3)(2sinx-1)=0

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Q: 2.1) SOLVE x²y" + xy² + (2x² - 2)y = 0 BY BESSELS METHOD

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Q: y(4) + ay" + by" + cy +dy = 0, here a, b, c, d are constants. Functions e-³2, e³2 and cos(√2x) are…

A: Given ODE with constant coefficients  is following :whose auxiliary equation is of the form .Given…

Q: Find all solutions to the following Diophantine equations. i. 35x + 25y = 8 ii. 35x + 25y = 15

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Q: SOLVE THE EQUATION. SHOW YOUR COMPLETE ANDCLEAN SOLUTION. (x – 2y + 5) dx - [2 (x – 2y) + 9] dy = 0…

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Q: d. The linear Diophantine equation ax + by = c has a solution if and only if dc. Let xo, yo be any…

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Q: y(4) + 18y" + 81y = 0

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Q: Find a particular solution to y" + 6y + 8y = -13te³t.

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Q: Solve for the particular solution using method of undetermined coefficient: (D² + 2D + 4) = 8 O Yp =…

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Q: Solve the Euler- Cauchy equation

A: We solve the given differential equation using Euler cauchy method.

Q: Let (xp, y,) be the solution of the following equations In 2 (2x)™² = (3y)n3 3Inx = 2lny %3D Then xo

A: Given equations are 2xln2=3yln33lnx=2lny

Q: Determine which of the following equations have integer solutions (x, y) = Z²: 1. 465x +4920y 1 2.…

A: Introduction: The linear Diophantine equation of the form ax+by=c has integer solution if and only…

Q: Solve the following equations by Ferobenius' method: x(x-1)y +(3x-1)y'+y=0 x²y-5xy'+9y=0 x²y+6xy'…

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Q: canonical form

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Q: max y = x1 2 + x2 2 ; subject to (x1 2 /25) + (x22 /9) =1 using the method of lagrangean .

A: Given function:- fx1,x2=x12+x22 Let gx1,x2 =x1225+x229-1

Q: dy dr +y- y²e* 4. Find the general solution of a.ye*(C + x) = 1 b. ye* (С — х) %3 -1 с. уе* (С — х)…

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Q: Solve the following system of equations by Newton-Raphson method y-sin(x+y)=0 x-cos(y-x)=0

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Q: What is the specific value of x and y in the diophantine equation 17x + 23y = 157?

A: In this question we have to find value of x and y in Diophantine equation,

Q: Q2\A: By using partial method solve 2x² cos x dx

A: Given :∫2x3cosxdx

Q: Find two solutions to 2y′′+ 5y′+ 2y= 0

A: for the homogeneous system, the auxiliary equation is given by

Q: Use Newton-Raphson method to solve the system x* + y – 1 = 0 y* – x +1 = 0 with the starting value…

A: We will use the following Newton-Rapson formula for finding the roots of 2 variable equations.…

Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. -t y(4)…

A: To determine the suitable form for Y(t) if the method of undetermined coefficients is to be used.…

Q: The values of m for which y = x" is a solution of x² y" – 7xy' + 12y = 0 are (Select the correct…

A: As the given value of Y is the solution of the equation that's why the value of Y should satisfy the…

Q: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

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Q: Find the general solution of the following system: 1 1 sint x' 4 1

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Q: Find the general solution of a²z a?z e*-y sin(2x + 3y) + y sin x ax² əy²

A: Given partial differential equation: ∂2z∂x2-∂2z∂y2=ex-ysin2x+3y+ysinx                        . . . .…

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y(4) +…

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