(a) By inspection, find a particular solution of y" + 2y = 10. Yp(x) = (b) By inspection, find a particular solution of y" + 2y = -4x. Yp(x)= (c) Find a particular solution of y" + 2y = - 4x + 10. y(x) =

Q: 2) Use y = ax to solve 2'y" - xy' + (x+1)y=0.

A: The given differential equation is: 2x2y''-xy'+x+1y=0. We have to solve using y=∑n=0∞anxn+r.

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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: Verify whether y(x) = 2e-*+xe-* is a solution of y" + 2y + y = 0.

A: Topic = Differential equation

Q: Show the solution using methods of undetermined coefficient. The answer should be Y = C1et + C2…

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Q: = Solvex (t) = Ax(t) where A 3 -2 [1] [8] = 4 and (0)

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Q: Find the general solution of x²y" + 10xy + 8y = x² Use the variation of parameters.

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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: Solve the following linear differential equation system, i.e., find y₂(t). dyn (1) dt dyż (t) dt =…

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Q: Determine general solution of: y(5) - 8y" = t² + 6t+4+et

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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: - Solve the equation z = x² + xy² when x = = 0, zz = y³ and when x = 2, z = y.

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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: Solve the ODE y(4) - 4y" + 8y" - 8y + 4y = 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: 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: Find the general solution of the DEs 1- f"(x)= y"(x)=12x +6x-8

A: The given differential equation is a second order differential equation so we will first reduce its…

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: 2x +y-z=3 x- y+z=0 y+2z =1. Then x=

A: Given system of linear equations; 2x+y-z= 3 x-y+z = 0    y+2z=1 We can use Cramer's rule to solve…

Q: 7. Solve for y 3(2y + 8) = 2x + 6

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

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Q: xy" + xy² + 4y = /Nx Find the solution y(x)

A: We will find the solution of the differential equations.

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

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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…

Q: Find general solution y = Yc + Yp of y(3) + y" 3e" + 4x2

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Q: ii) y" - 3y'-4y = 2x2-3.

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