Use the method of reduction of order to find a second solution to t’y'" + 2ty' – 2y = 0, t > 0 Given y1 (t) = t Y2(t) = %3D

Q: y" + y = sin x %3D

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Q: x² - 4x +6 4 X Find y' if y=- y'=0

A: Given query is to find derivative.

Q: (x2 – 1)y" – 2xy' + 2y = 0 - tion ofS the o uation

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Q: y" +y' – 2y = 4e* – 2x

A: We have the given differential equation is y''+y'-2y=4e-x-2x2     …..(1) The auxiliary equation for…

Q: Given the initial condition y(0) : e–2y = y'? 3, what is the particular solution of the equation…

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Q: Use the method of reduction of order to find a second solution to ty''−(6t+4)y'+(9t+12)y=0,  t>0…

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Q: Find a general solution of y'" = (- 50 – 50 i /3) y. ... y(x) = C, e +c2 e-

A: The given differential equation is y''=-50-50i3y Demoiver's theorem for fractional power  If rcos…

Q: 1. For each F(s) = L{f(t)}, find f(t) = L-'{F(s)}. %3D 1 а. F(s) — s2 – 7s + 10 4s b. F(s) s2 – 4 3s…

A: Given that: c. F(s)=3s-4(s-1)(s+2)2

Q: (t+2)y"-y'-(4t+10)y=0 Given y1=e-2t Find y2?

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Q: Verify the DE when y' = 9sqrt(xy) equals to y = (3x^3/2 + C)^2.

A: The given differential equation y'=9xy We have to show that y=3x32+C2 is the solution of the…

Q: 1. For each F(s) = L{f(t)}, find f(t) = L-'{F(s)}. %3D 1 а. F(s) — s2 – 7s + 10 4s b. F(s) = s2 – 4…

A: Student asked to slove for part e.

Q: Use the reduction of order to find the general solution 21. xy" - y - (x + 1)y= 0, y₁ = e. (0,00).

A: By using method of reduction of order we solve the given ordinary differential equation.

Q: y' =xy

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Q: If the solution of y' = 2(2x - y) passes through the point (0,1), determine x when y = 7.

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Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: x?y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 2. Given that yı(x) = x is the first solution of Equation…

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Q: 1 Separate variables to find a solution a. yy' +36x=0 b. y'=1+4y², y(1) = 0

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Q: 1-t For which functions does y' ? Select all that apply.

A: Given that  y' and we find a function f(x,y). Here i attached solution of this question.

Q: y'- Sy: x² e^ - x. 5* cs

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Q: Find y' for y = 9x-6 + 7x¯1. y' =O

A: Given: y=9x-6+7x-1

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: 2x³y' = y(y² + 3x²) a. y-2x2 -x +c b. yx3 -x + c C. y2x x3 -x+c d. y'x2 = -x +c

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Q: Solve: x"-x+ 5 y'=t y" - 4 y-2 x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A: Solution:

Q: For y(t) solution of y'=-4y(1-y/4)+3 find the intervals where the function of t is increasing or…

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Q: Solve: x" -x+ 5 y'=t y" - 4 y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: (4) Find y' if y = xcot-12x -V1– 4x².

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Q: Find y' for y=8x7 + 4x¯¹. 1 y'=0

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Q: Solve. y" + 36y = u;(t), y(0) = y' (0) = 0 %3D S f(t) for t < 5 1 9(t) for t 5' The solution can be…

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Q: - 1 Find y' for y = 7x-4 + 2x-1. y' =

A: We havey=7x−4+2x−1

Q: Find the particular solution: y': 3(x² + √x) yez , y(4) = 0. ans

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Q: * If y" = 9x – 6x² ,y'(2) = 4, y(2) = 12 ,find y %3D

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