Solve the equation Ax=b by using the LU factorization given for A. 2 -5 2 2 -5 2 8 -6 12 - 1 -3 10 O -3 5 b 12 4 -7 2 -11 0 1 4 Let Ly -b and Ux =y. Solve for x and y.

Q: find general solutions (for x>0) of the Euler equation x3y3  -3x2y"+xy'= 0

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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: a) Find the general solution of the given equations of the line (2x - 5y + 10)dx+ (7x + 3y - 8) = 0

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Q: 2. Show that each of the following equations has a solution of the form u(r, y) = ea+By for some…

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Q: 1. Solve the following first-order equation: (2.ry +3y?)dr - (2ay+a)dy = 0. %3D

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Q: find general solutions (for x>0) of the Euler equation x3y3+6 x2y"+4xy'= 0

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Q: Solve the equation Ax = b by using the LU factorization given for A. - 6 4 0 0 4 -6 4 6 A = - 12 16…

A: Ans _ A=4−64−1216−78−104=100−3102−114−640−25001 and b=6−82Let l y = b100−3102−11y1y2y3=6−82y1=6 —…

Q: Q14- Solve the equations to find x, y, z by Gaussian elimination : 3 x+z = 4 2 -3 x+3y - 2 5 X - 5 =…

A: Given: The given system of equation is,

Q: Find a general solution of the equation: 5xy' = 2 – y %3D

A: Please find attachment for the details solution

Q: Uk+2(x) – 3k. dx duk+1(x) d²uk + 2k(k – 1) 0, (8.295) dx2 has, in the x variable, the structure of a…

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Q: Solve this differentlal equation: dy 0.13y(1- dt 400 y(0) 5 yu-- e (400-) syntax error: you gave an…

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Q: z1 = 2 + 4i 22 = 5e2i Z3 = 4 cis 40°

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Q: a) Give a particular solution for y" – 2y' + y = 3e*. b) Give a particular solution for y" – 2y' + y…

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Q: 9. Solve the Bernoulli equation y' – 5y = --žxy³. (Hint: Try substitution u = y=²).

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Q: Find the general solution of (xe +y)da – cdy = 0 %3D

A: Given differential equation is xeyx+ydx-xdy=0 we can write it as dydx=yx+eyx             (1) which…

Q: 2. Solve for the values of w(t), y(t) and z(t). w" - y + 2z = 3et -2w' + 2y' + z = 0 2w' – 2y + z' +…

A: Given system is w''-y+2z=3e-t-2w'+2y'+z=02w'-2y+z'+2z''=0with   w0=1, w'(0)=1, y0=2, z0=2, z'(0)=-2…

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: A second order Caushy – Euler equation having a solution y(x) = x-2cos(4Inx) is x?y" + 5xy' = 0 O…

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Q: Solve for z. If there are no solutions type DNE: 1 -4%3= I- 4 4z - 16

A: x4x-16-4=1x-4

Q: 47-50 Find dw/ax, dw/ay, and du/dz. 49. w = =x²+y² + z?

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Q: 3. Find the general solutions of, x+y dx x-y, a.

A: We have to solve the given differential equation.

Q: z.e +4 a'z cos(2x+y) z.e Solve ax 4 əx-əy axəy

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Q: find general solutions (for x>0) of the Euler equation x3y3 +3x2y"+xy'= 0

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Q: find general solutions (for x>0) of the Euler equation x2y"+xy'+ 9y = 0

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Q: 2- X-J =(M(404) 3x उ्रुफट (X) %3D gu) =x°-8e

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Q: 3x'y"+2xy' = 0 %3D

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Q: 3. Determine the values of the variables to satisfy the equation using a) Jacobi and b)…

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the remaining as…

Q: 1. a) Find , if y= (x² – 11)“ dx b) Express (8/30) (2Z60) in the form a+ bi c) Solve (2+3) +3/- x+iy…

A: The detailed solution is as follows below:

Q: 1 I. In x dx + C - In x dx 1 -In x + C 2 II. O Both equations I and II are TRUE. O Only equation I…

A: Given:  I) ∫ln x dx     Apply integration by parts:             ∫fg'=fg-∫f'g here f=ln x, g'=1…

Q: 4. Which of the following is a Legendre's equation? a. (1-x²)y" - 2xy' + 3y = 0 b. (1-x²)y" + 2xy' -…

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

Q: 5. = y – xy³e-2x у —

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Q: Question 13 What is the value of B in 4x+6r+4 Jz(2+2r+2) B(2x+2)dr dx = Adz + +2z+2 Cdx a2+2x+2 %3D…

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Q: Solve the equation Ax = b by using the LU factorization given for A. 4 - 4 4 1 0 0 4 -4 4 - 4 A = -…

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Q: Now, we can set zy = 0, substitute 2x for y, and solve for x. + 21 = 0 = -21 X =

A: Substitution method: - The substitution technique could be a simple approach for determining linear…

Q: find general solutions (for x>0) of the Euler equation x2y"+7xy'+ 25y = 0

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Q: 1-find the value of z and x, 2- find (A") + d* (x². e3*) 3- find (A+ 3 lm 3), 4- 2A*A", 2r + Z+ y= 2…

A: Given: The equation are  2x + Z + y = 2 x - Z + 4y = ln 1 x + 2y - 2z = 4

Q: Find the general solution to the equation 4(x^2)y''+8xy'+y=0 by the method of Frobenius.

A: The differential equation is 4(x2)y''+8xy'+y=0. Let the solution be y=∑n=0∞anxn+r, then its…

Q: 5. Find the largest constantr so that o(x) = e"¤ is a solution to %3| y" – 2y" – y' + 2y = 0. -5 1 O…

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Q: The Cauchy-Euler equation can be reduced to an equation with constant coefficients by means of the…

A: For the solution follow the next steps.

Q: Ex/solve The equations 2x-y+3Z= -5 using Sing Gram e %3D X+y - Z = - 1 -2x+3-2Z%3= 2 。 メ= -1 -2 -1…

A: 2x-y+3z=-5x+y-z=-1-2x+y-2z=0 by using Cramer's rule- x=D1D, y=D2D, z=D3D D=2-1311-1-21-2…

Q: Solve the equation Ax = b by using the LU factorization given for A. 100 2 -2 -4 A= 1 -2 2 -2 -4 1 0…

A: Since multiple questions are there, we will solve only the first one. If you want the answer to the…

Q: Show that the homogenous equation (Ax + By) ⅆx + (Cx + Dy) ⅆy = 0 Is exact if and only if B = C.…

A: Please refer the attached image for complete solution.

Q: 7. Solve the Bernoulli Equation r +y² = ry dr

A: The Bernoulli equation is x2dydx+y2=xy. Calculate the value of y.

Q: 1. Determine the values of the variables to satisfy the equation using Jacobi. 5a - 2b = 40 Ans. a =…

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Q: Solve the given O.D.E. by the method of "Variation of Parameters"; 1 Y" - 4 Y' + 4 Y = [12 x2 -…

A: The solution is given as

Q: Solve the variational problem 8 Ix (y ? +2y (x+y)] dx = 0, given y (1) = y (2) = 0. %3D

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Q: Now consider the fourth-order equation Yk+4 + Yk = 0. (4.76) Its characteristic equation is (n² +…

A: Differential equation is given, we have to find the determine step.

Q: Solve for z in the equation 2-5j z+j+1 2= +3j 2z-j A) 0.2 + 0.1 j B) -0.2 + 0.1 j C) 0.2-0.1j D)…

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Q: Solve the variational problem 8] +2y (x +y)] de = 0, given y (1) éy (2) 0. %3D

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Q: e 3z -で dz (ez + e5z)2 I = 0,

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.