Let y be the solution of y'+y=x, xER,y(-1)=0. Then, y(1) 류를 ²-28² 2-2e -

Q: give me the solution of   y'' - 2y'- 2y = 0

A: Topic:- differential equation

Q: d) Solve: y"+y"-5y' + 3y = 0

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Q: Solve: x'y" - 7xy' + 41y =0

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Q: y” – 10y’ + 25y = 30x+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: Find all functions y satisfying y" + y" = y' + y. You may use the factor- ization x + x² – x - 1 =…

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Q: (2xy² + 2y) + (2x²y + 2x)y' = 0

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Q: Solve (D² – 3D + 2) y = 2e3 +4 sec (e-)

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Q: Find the general solution by undetermined coefficients.  y'' + y = 2x2e-x.

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Q: Eliminate the arbitrary constants of the equation y = Cje 2x + A y" - 2y' - 3y = 0 B y" - 4y' - 2y =…

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Q: Find the general solution for: y'' - 4y' - 5y = -6xe(-x)

A: We need to find the general solution for y'' - 4y' - 5y = -6xe(-x). ---------(1)Idea: First, we will…

Q: u" - 16u = 0

A: Given the differential equation is u" - 16u = 0. Here the auxiliary equation is m2 - 16 = 0

Q: By Lagrange's formula, prove that y =y3-0-3(ys-y- 3) + 0-2 (y_ 3 -y_5).

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Q: The general solution of y' x2 can be written in the form

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Q: d'y (3x-5)(2x + +9x=6) Determine the and of y = 7x Solution:

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Q: Find the general solution x²y" - xy + y = x lnx

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Q: Suppose that Yı x5 is a solution to x²y" – 10xy' + 30y 0. Use reduction of order to find another…

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Q: Find a real general solution x2y"+0.7xy′−0.1y=0

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Q: Find the General Solution: y" - 3y' + 2y =4e ** -4x

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Q: Solve y'' − 4y' + 4y = 3e2t

A: Solve y'' − 4y' + 4y = 3e2t

Q: If x, y belongs to Z prove that the equation x^2+4x-8y=11 has no solution

A: The given equation is, -----(1)

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: Find a particular solution to y" + 5y + 4y = -10te". Yp =

A: Given the D.E. y''+5y'+4y = -10te3t We have to find particular solution yp of this equation.

Q: Solve zx+zzy= 2x, z(0, y) = y

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Q: Is (y − 33)2 = 4a(x − h) the solution to the diff. equation (y-33)y''+(y')2 =0

A: soln:Giveny-332=4ax-hdifferential equationy-33y''+y'2=0

Q: 5) x2. dx = x² + 3xy + y², (c) dr = 2 = 3v, + 3x' (d) (1 - y)' + By - 5x = 0.

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Q: 4. (-9) h()== In dx

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Q: - 4. 3y(x² − 1)dx + (x³ + 8y − 3x)dy = 0; when x = 0, y = 1

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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: Solve x'y-5xy+13y-0

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Q: 1.² T 20 40x-x² 9√x²+y2 dydx=

A: We have to solve ∫020∫x40-x29x2+y2dydxThe region bounded by0≤x≤20x≤y≤40x-x2⇒x=y and y=40x-x2squaring…

Q: j'+7y'+12y=2le", y(0); (0)=,"'(0)= -10. 10)=-10 .

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Q: y' = 11y 2; y = 3 when x= 2 (Type an exact answer, using radicals as needed.)

A: We will integrate the following using the separation of variables method. Then we will find the…