Q2) find the solution of: A) yk+3 +4yk+2 - 5yk+1=0 ,yo=4 , y1=-7,y;=23

Q: Show that rejst =rcjs(-0)

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Q: When solving Jx² + 4y? = 16 Lx² - y? = 1 %3D by the addition method, we obtain y² = 3, so the…

A: Given that, x2+4y2=16x2-y2=1 And solution is y2=3

Q: 5olve The simultaneaus.equation 22 tiw - 2 2+ (1ti)w =3;

A: Given :                    2z + i ω = 2 .................(1)2 + (1+i)ω = 3i ..............(2)then we…

Q: Show that the equations xp- 4yq=0 and (32 +2z +1)(p+q)=x'(x+4y) compatible and solve them.

A: 1. Two partial differential equations of first order are said to be compatible if they have a common…

Q: , Find the solution of 4x²y" – 6x²y' + y = 0, x > 0 of the form Y1 = ="(1+cqx+ Czx² + czx³ + • . ·)…

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Q: Use the separation of variables method to solve 4urz = Utt, H 00 ur (2, t) = 0 ur (0, t) = u(x,0) =…

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Q: solve by the method of undetermined coefficients. b.) y''+4y=5sin(4x)

A: We need to find D.E.

Q: Solve for the value of x, and x, using Gauss-Jordan Elim. x,-5x, =-4 7x, – x, = 6

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Q: Find all solutions of y'= 3y. Which solution satisfies y(0) = 9?

A: Given differential equation is y'=3y. To find all solutions of y'=3y which satisfies y0=9. Solution:…

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: Solve the IVP *y" – 2ty + 2y = 4t², t>0, y(1) = 1, y(1) = 5

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Q: 2) Does the equation 2x + 6y = 35 have any solutions where both x and y are whole numbers? Why or…

A: The given equation is  2x + 6y = 35

Q: Find the general solution. 4. (4D3 - 3D? + 1) y = 0

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Q: 2- Solve the following equation: Utt = c?uxx +, u(0, t) = u(2, t) = 0 u(x,0) = x? ,u; (x, 0) = e*

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Q: Solve for s in terms of r, t, and u. t = -rsu

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: What is the particular solution for y′=6ex+7x3−7x+1 such that y(0)=−4?

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Q: Solve the IVP y′′ + 4y′ + 13y = 0, y(0) = 1, y′(0) = −5

A: To  Solve the IVP y′′ + 4y′ + 13y = 0, y(0) = 1, y′(0) = −5

Q: Use the substitution ux)%3D2х - Зу (x)+2 to solve the following IVP: У'+ (2х - Зу +2)23D0, у (0) —2

A: Given that diffrancial equation y'+2x-3y+22=0  , y0=2Solutiondydx=-2x-3y+22let…

Q: 1. Solve ,analy hically., the fallowinng differencerequ. a. C- YCK+3) +2 y(km2) +oi45y(k+i) +0105…

A: As you require, we will solve this question on the given difference equation purely analytically.

Q: The solution of the IVP, y' = -2xy, y(0) = 2, is: %3D

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Q: Use undetermined coefficients to find the particular solution to y'' + 4y' – 4y = 7t² + 4t + 6 Yp(t)…

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Q: Solve for u = u(x, y). Uyy + 10uy + 4lu = 5e5y. NOTE: Express the answer in terms of c1(x) and…

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Q: Solve the IVP: y" –- 6y' – 7y = 0, y(0) = 4, y' (0) = 4 %3D

A: First we will find the auxiliary equation of the given homogeneous linear differential equation with…

Q: find the genral solution (D +2D,D, -2D, +2)u = 0

A: Given  Dx2+2DxDy-2Dy+2u=0   …………………(1) Consider the equation F(Dx,Dy)u=0 Here F(Dx,Dy) =…

Q: Solve the IVP y' = [, y+,yc0) = [2]. [et y + -1 3.

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Q: Find the solution of with y(0) = 8 and y'(0) = 7. y = y" + 3y + 2y = 72e²t

A: 1f(D) eat = 1f(a)eat .

Q: Solve in terms of t, u"""" + u"""' = 0.

A: Given the differential equation is u"""" + u"""' = 0.  Here the auxiliary equation is r8  + r7 = 0.

Q: To solve the sgstem in the methat of eliminating variables, x+y +Z =2 X +2y-Z =6 2X +y-Z =5 of

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Q: Find the particular solution Use method of undetermined coefficients. 1. y + 9y = 81x² + 14cos4x;…

A: As per the instruction, we will be answering only the first one. For (1), The characteristic…

Q: Solve the given differnetial equation by undetermiend coefficents  y'' + 2y' = 2x +7 -e-2x   y(x)…

A: Given:-           The differential equation  is:…

Q: Show that the equations xp – 4yq = 0 and (32 + 2 +1)(p+q)=x°(x+4y) are compatible and solve them.

A: 1. Two partial differential equations of first order are said to be compatible if they have a common…

Q: Solve for the solution set using Gauss-Jordan Elimination x + y + z = 2 - x + 3 y + 2 z = 8 4 x + y…

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Q: Use back-substitution to solve the triangular s 5x - 5y + z = 0 y + 5z = 21 Z = 5 (x, y, z) =

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Q: Obtain the general solution. (D^3 - 4D)y = 0 when x = 0, y = 0, y' = 0, y'' = 2

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Q: Solve the IVP: y" + y' = 0 y(n) = 0, y'(1) = 2, y'"(n) = -1

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Q: solve the sysyem  5x-y+2z=3 4x+5y+7z=26 x+y+4z=3 The solution is, (type an ordered triple)

A: Given equations:                               5x-y+2z=3       ....... (1) 4x+5y+7z=26…

Q: How many solutions are there between planes P₁: 2xy + 2z = 2 and P₂: -x + 2y + z = 1? If there…

A: Given is the equation of two planes. The objective is to find the number of solutions between the…

Q: Solve by the substitution method. 2х — 5y %3D 8 x = 4y + 4 (х, у) %3

A: We have to find value of x and y by substitution.

Q: What points (x, y, z) satisfy the equations x2 + y2 = 4 and z = 3?

A: Given: x2+y2=4, z=3

Q: 5. How many solutions are there between planes P₁: 2x -y + 2z = 2 and P₂: -x +2y+z=1? If there…

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Q: Consider the following IVP: y" + 3y' + 2y = 12x2; y(0) = a, y'(0) = b Find the solution.

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Q: Solve the give differnetial equation by undetermined coefficients y''' - y'' -16y' + 16y = 5 - ex +…

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Q: How many solutions are there between planes P₁: 2x -y + 2z = 2 and P₂: -x + 2y + z = 1? If there…

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Q: = 3e2x and y,, = x² + 3x are respectively solutions of у" - бу' + 5у -9е2х y" – 6y' + 5y = 5x² + 3x…

A: General solution y(g)= y(h)+y(p)

Q: (y³ – 3y + 2)/9 + x²dx + x²dy = 0

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Q: The solution of the IVP y" + 9y=0, y(0) = 1, y'(o) = 0, is %3D

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Q: 3) xle), ale), zl4) genecal solutions? 3x+G4-22 %3D - 2y

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Q: Use the separation of variables method to solve 4urz = Utt, H 00 ur (0, t) = ur (2, t) = 0 u(x,0) =…

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