se method of refuction of order to find a second solution y2(x). Given that y1(x)=ex is a solution. (x(4)-4x)y'' + (4-x(4))y' + (4x-4)y =0

Q: Solve: (3x – 2xy+ 3y)dx = 4rydy (y +3x)(y – x)3 = Ca³ %3D O (y + 3x) (y – x) = Ca³ (y – 3x)(y + x)3…

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Q: If a, ß and y are the roots of the equation, x³ - x - 1 = 1 + a 1+ B + 1 - α - 1- B + 0, then 1 + y…

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Q: Which of the following is the standard equation of 9y² – x² + 2x+ 54y+62

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Q: y = (1– 2x) ;y" ¡y"

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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 x²y" - xy + y = x lnx

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Q: Solve the difference equation: 3 (²7) y[n+ 2] - n> 0 y[0] = 10 and Y y[n + 1] + y[1] = 4 n (1) ₁…

A: Given difference equation is ,      yn+2-32yn+1+12yn = 14n   ;  n≥0     ;  y[0]=10  and  y[1]=4 (.)…

Q: (x²-x) y¹ = (x²+1) y + 12x (x²-1) ³ y' when x = 2, Y = 9

A: Given differential equation is  x3-x y' = x2+1 y  + 12 x x2-13                      ⇒      x3-x…

Q: Find the solution. (4D³-3D + 1)y=0 A y = (₁+₂) ²¹/²+c₂e² Get ® By y = (c₁ + ₁₂x) e */2² + c₂e²r x/2…

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Q: x(0) = -2 () 30 If y(0) I and y(1)-2, what is x(0)?

A: Let

Q: In(-/-) (vi) 2x In - x = 0

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Q: Q1: If y" + y = x², then yp = Q4: The solution of y(4) - 5y" + 4y = 0 is: (B) c₁e* + c₂ex +…

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Q: Find the general solution of (x+ 1)² -2(x+1) 9-(x²+2x-1) y = (x+1)² e*, y₁ = (x + 1)e is a solution…

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Q: of the form ₁ = x²(1+₁x + ₂x² + 3x³ + ...) Enter C1 = Find the solution of 4x²y" + 6x²y + y = 0, x>0…

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Q: Find the solution of 4x²y" - 6x²y + y = 0, x > 0 of the form Y₁ = x¹(1+₁x + €₂x² + 3x³ + ...) Enter…

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Q: -5x +3x – 28 dx (x – 1)(x² + 9)

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Q: Find the general solution to y(4) – 6y " + 8y" = 0. In your answer, use c1, C2, C3 and c4 10 denote…

A: The detailed solution is as follows below:

Q: Solve 1 0-²40 = 5 x (0) = - 4, y(0) = 10

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Q: Solve y+y = 1, y (0) = 4 Oy² = 1 +7e-² Oy = 1+7e-² Oy² = 1 +7e-² Oy = 1+5e-² Oy = 1+7e²

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Q: Solve for X if (x)=z=r

A: The given expression xy-z=rw. We have to solve the expression for x.

Q: y(4) + 3y" - 4y = 0

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Q: Determine the solutions of: y^n  + 4y  = 0 y(-π) = y(π), y´(-π) = y´(π)

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Q: If u(x) = x3, then du = 3x2.

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Q: 3(y+7)-7y=1 y=

A: First we distribute 3.

Q: Solve 1. (z - 4) s(3z + 2) 2. X+8(x+1) > 3(2-x)+x

A: Given; 1.  (8/6) (z-4)<=(2/18)(3z+2) 2.  x+8(x+1)>3(2-x)+x

Q: 2. Use undetermined coefficients method to solve 1 yi = 4yı + 2 - 3e", y2 = 9y1 + 6y2 + 10e'.

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Q: (2) x (x+3)y"+2y'+y=0 solve for yox)

A: To solve the differential equation: x(x+3)y''+2y'+y=0 We can start by assuming a solution of the…