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

Q: Find two linearly independent solutions of 2r2y"- xy' + (-4x + 1)y = 0, x > 0 of the form Y1 = r (1+…

A: Given fill in the blanks have already some data, it is wrong as per given question. I solved it, and…

Q: How to solve this equation y'''+2y''+4y'+8y=(5e^3t) + 1 using Variation of Parameters with wronskian…

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Q: Q: Find the solution of x, y, z by using Gramer's Rule. 3x + 2y - z = 1 x- y+ 5z = -2 2x + y = 3

A: The given system of equation is  3x + 2y -z =1 x - y +5z =-2 2x +y =3

Q: 5. Find a general solution to the Cauchy-Euler equation x?y" + 7xy' + 9y = 0, for x > 0.

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: use the Lagrangian method to solve:   U=(x+3)(y+5) given 30=3x+2y

A: Given the relation 30=3x+2y. We need to minimize the value of U = (x+3)(y+5). Substitute the value…

Q: Solve: dy 6- y") +. onn 13-1 Ordineiy Dibgerential equation

A: The solution of the differential equation can be found with the help of the separation of the…

Q: 3. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solution of y" + 4y = 0?…

A: Given, y''+4y=0 a second order differential equation. To show that y(x) = C1 sin 2x + C2 cos 2x is a…

Q: 2. Solve dx2 d²y for x = u? + 1 and y = 3u3 – 3u in terms of the parameter u. -

A: Given query is to find indicated derivative.

Q: Solve a & b with given A[r = 3x şax+ (y + z + 3) Ay +(6x - z³) a₂] where: np = ax + 4ay - 2az 2+y³

A: Given

Q: Find the wrong Kian W(y1,y2)(t) of y1 and y2  Where y1=t and y2= e^t are solutions of…

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Q: Let y(x) be the solution of y' = y − 6x such that y(2) = 2. Using a step size of 0.5, set y0 =…

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Q: 8. Find the partic ular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: We have to find the particular solution of x2y''+xy'=1 ; y=0 and y'=12 when x=1.

Q: t with y(0) Solve y + 5y ing %3D 4 express- the particular solution as a convolution.

A: In this question, we have to find the particular solution of the differential equation by help of…

Q: Verify that y, = e2x and y2 = e5×are solutions of у" - 7у' + 10у %3D 0

A: We have to verify that the functions y1=e2x and y2=e5x are solutions to the given differential…

Q: Use variation of parameters to find a particular solution of the DE y/" – 4y + 4y then write down…

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Q: 1. y" + 4y'+ 3y = 12 В. 12 А. 4 С. -4 D. 4x

A: Given y''+4y'+3y=12(D2+4D+3)Y=12Auxillary equation is m2+4m+3=0Upon solving, m=-1,-3CF,…

Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

Q: (r²+y + y³) dx – x dy=0

A: →∫1a2 + x2dx  = 1atan-1xa→ddxuv = udvdx + vdudx

Q: Q Find the solution of x, y, z by using Gramer's Rule. 3x + 2y - z 1 x- y+5z = -2 2x + y = 3

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Q: Use the method of Variation of Parameters to solve. SHOW WORK. y" – y' – 2y = 2e-t

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Q: 7. Eliminate a and b from the equation y =- In(ar +bx) where a,beR-(0}

A: q-7 eliminate a and b from the equation y=12lnax2+bx  this can be written as 2y=lnax2+bx⇒e2y=ax2+bx…

Q: Use variation of parameters to find a particular solution of 14aie" 3 y" – 2y' + y - Yp(x)

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Q: 3. 2y" + у' - 3 А. 3 В. Зх C. 3x D. x?

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Q: Find the general solution to the DE using the method of Variation of Parameters 8 y" – 4y = e2x + 1

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Q: How do I solve this Bernoulli equation using P(x), Q(x) and n as well as u(y)?

A: First, we write it in form of Bernoulli Differential equation.

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

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Q: Solve the Bernoulli's DE: 2x3 y = y(y? + 3x2). %3D

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Q: dy 1. dr + 3y = 2xe -3z %3D

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

Q: We wish to find the solution to =26y that passes through the point (x, y) = (1, 3).

A: Explained below

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

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Q: 3. Let u(x, t) be the solution to 5ætu, – ut = 0, u(x,0) = 3x², x > 0 - obtained using the method of…

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Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: If integration using u-substitution technique is used to solve for O u = e4x Ou=1-e¹ O U= u = €²x…

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Q: Solve the given IVP for the Cauchy-Euler DEQ t²y"(t) – 4ty'(t)+ 4y(t) = 0; y(1) = –2, y'(1) = -11…

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Q: Obtain the general solution valid near the origin: 2y" + 9ху' — З6у %3D 0

A: Power series solution of the differential equation

Q: (D* – 4D³ +14D² – 20D +9)y = 0 - -

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Q: 2. Find te gunural soiUtion of 2

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Q: Find the solution of Uy = 36 ut + 10 u if Ux U₂ (x,0) = 3e-2t using the method of separation of…

A: Given partial differential equation is ux=36ut+10u____(1) and given condition isux(x,0)=3e-2x We…

Q: 2 Verify that for r > 0, y = r is a solution to yy = x. V3

A: Double differentiate to prove the given

Q: (D³ + 2D² − 5D − 8)y = 0, when x = 0, y = 0, y' = 0, y = 2 - -

A: Given  (D3+2D2-5D-8)y=0 and when x=0, y=0, y'=0, y''=2. The formula for differentiation is…

Q: 2. u(z) +

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Q: 8. y" - 4y' - 12y = 3e А. 3/7 e %3D В. Зе C. -3/7 et D. -7e

A: Given: Differential equation is y''-4y'-12=3e5tTo obtain the particular integral of the differential…

Q: 3. Find the complete solution of the giyen DE using the Method of Variation of Parameters: y" + 44…

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Q: The solution of the IVP t(t + 4)y + (t + 4) y =t, y(2) = 2 exists in the interv

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Q: (b) Find the general solution of: = yx² - xy ax Given z = y when x=1, determine the particular…

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Q: Find general Solution of y + +y+ 4y = Ct1)e Using method of vanafion.

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Q: 3. Find the genesral Solution: y* 5y^ +3y' -ay=

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Q: Find the solution of BVP 2. Uxy = 4xy+ex ; uy (0,y) = y, u(x,0) = 2

A: uxy=4xy+ex uy0 ,y =y u(x,0) = 2 To find solution of given differential equation

Q: Solve the second-order DE y"+2y'+4y= g(1), y(0)= 0, y'(0)=1, where 2, Ost<2 g(1) ={-2, 2si<4 0, 124.

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