Find the general solution of the fifth-order DEQ. 2x(5) – 7x(4) + 12x" + 8x" = 0

Q: 24- ex +12x²-6,yc0)=2, yo)=3

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Q: Find the 2nd solution by reduction of order. y" - 4y + 4y=0; y₁ = e²x

A: Here given the differential equation as y''-4y'+4y=0 .......(1) And it's one solution is y1=e2x

Q: Solve the initial value problem. dt t-1 = 4, r(1) = 5 %3D Or-+7t + 15 6. -55 Or + 7t - 5 r= 3t + 7t…

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Q: In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y" – 4y'…

A: Given Differential equation, y''-4y'+4y=18te2t-2e2t-8t The auxiliary equation of this…

Q: Solve the initial value problem -4sin(2t – 4), s'(0) = 100, s(0) = 0. %3D %3D dr2

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Q: . Solve the yn+2+4Yn+1-5Yn coefficients = n2"+2" using method of undetermined

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Q: SOLVE X²y" + xy² - (4x² + 1 ) y = =0 BY BESSELS METHOD.

A: As per the question we are given a second order linear homogeneous differential equation and we have…

Q: Find the general solution of the following DE in explicit form. y'=2+2y-2x +8

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 2. Find general solution of the DE y" + 3y" + 3/ + y = 0

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Q: x'y" – 3xy' +4y=x° Inx

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Q: П. Solve xау + (3х 2y)ax = U in two ways

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Q: wouldn't there be a t in the second term of the general solution?

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Q: 11.2) SOLVE : 5x²y" + x (1+x) y ² - y = 6 by Frobenius Method

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Q: Find the general solution of i = Ax, where A = .

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Q: 4) Find the solution of y'= 2(2xy) passing through (0,1).

A: Given, Equation  y'=2(2x-y) passing through a point (0,1).

Q: 4. y" - 5y' + бу %3 -sin(2x)

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Q: 19. Show that yı = 1 and y2 = /x are solutions of yy" + (y')² = 0, but that their sum y = y1 + y2 is…

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Q: Find the general solution to xy′′−3y′=0.

A: We have to find the general solution of the given differential equation.

Q: Solve the initial-value problem. x²y' + 2xy = In(x), y(1) = 5 %3D

A: givenx2y,+2xy=ln(x), y(1)=5y,+2xy=ln(x)x2this is a standard form of linear diffrenetial…

Q: Find a general solution of y"- iy'+6y= 0.

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Q: Find the general solution of the following equation valid near the origin: (1+4x²) y¹¹-8y=0…

A: Given: Let us consider the given differential equation, 1+4x2yιι-8y=0

Q: Find the general solution of: az əz 2, дх ду (1+ /z- x – y)

A: The given equation can be written as: 1+z−x−y∂z∂x+∂z∂y=2dx1+z−x−y=dy1=dz2          ......i

Q: 1. Determine all possible solutions of ²u ex² = d²u oy ² by using variable separable method. 7

A: The given problem is to solve the given partial differential equation by using the method of…

Q: х2у" + x(x-1)у' + (1-x)у %3D 0

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Q: Find a homogeneous LDE with constant coefficients that has y=-1+3x²e* as a particular solution.

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Q: Find the general solution of ди ди (y – z) + (x – z) ди + (2y – 2x) ду - az

A: The differential equation is given as (y-z)∂u∂x + (x-z)∂u∂y  + (2y-2x)∂u∂z = 0 We will solve it by…

Q: Find the general solution of (3D2 + 5DD' - 2D'2)Z = 10 cosh(2x + 5y).

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Q: 6. Use undetermined coefficients to find a general solution of -2x y" + 5y' + 6y = 3e¬2= +e3z

A: The given differential equation is y''+5y'+6y=3e-2x+e3x

Q: Solve the given initial-value problem. -2 2 X'= × - (- ~~ ) x + (²) X 3 4 2 X(t) 2t 6e-6e²t - 6 X =…

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Q: The equation X2 - 19Y² = 13 has an integral solution, i.e., there is a pair hat x2 19y2= 13. (proof…

A: We have to solve given problems:

Q: Find the general solution to the homogenous DE y'-16у' + 64у %3 0

A: The given homogeneous DE is y''-16y'+64y=0. The auxiliary equation is m2-16m+64=0.

Q: Find the solution of (1 + e²)yy = eª that passes through (0, 1).

A: (1+ex)yy'=ex(1+ex)ydydx=exseparation of variablesydy=ex1+exdxIntegrating both…

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

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Q: The general solution of 5uxx – 6uxy +uyy = 0 -

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Q: - EXAMPLE 3 Find the particular solution of 3xy' y = lnx + 1, satisfying y(1) = -2. x > 0,

A: It is a first order differential equation.

Q: Verify that y = c1x+c2Vx+ is the general solution of the 6x following nonhomogeneous 2.²y" – xy' + y…

A: Derivative of xn: Derivative of an exponential function that is, xn is given by the formula,…

Q: The solution of the nonhomogeneous DE y" + 4y' +4=5e* is

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Q: Use the method of undetermined coefficients to solve the initial value problem x''+4x=3cos2t  ;…

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Q: Show whether the two equations y₁ = using the Wronskian. 12e and y2 1.2e are independent or…

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Q: 5. Find the particular solution of x²y' – 2xy = x* + 3; where y = 2 and x = 1

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the particular solution of: y' – 4y = x²e* that satisfies y(0) = 2.

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Q: Find general solution of the DE 4y′′′ + 4y′′ + y′ = 0

A: The given equation is 4y'''+4y''+y'=0. The characteristic equation of the given differential…

Q: Find the general solution. 6y(4) + 7y" – 12y" – 3y' + 2y = 0 SHOW WORK.

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Q: 10. Find the particular solution that satisfies the initial condition. xy'+ 2y = 3x² – 5x. Initial…

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Q: 22. Find the particular solution for he non-homogen 1st OLDE using undetermined coefficient method,…

A: Differential equation system.

Q: 5. Find the particular solution of x²y' – 2xy = x* + 3; where y 2 and x = 1

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Q: Find the general solution of y" + 2y=ex +2.

A: The Auxiliary equation is D2+2=0 solve for D Therefore  D=±-2=±2i Therefore the solution is…

Q: Use the Gauss-Seidel iterative technique to find approximate solutions to 3x_1-x_2+x_3=1,…

A: According to the given information, it is required to find the approximate solution of the given set…

Q: 1 Find the general solution of x'y" +xy' -y= x+1

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