Use Variation of Parameters to solve the Initial Value Problem. y" + 6y' + 9y = 3e", y(0) = 3, y'(0) = 3 %3D

Q: Solve y" + 3y" – 3y' – y = x+ e².

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Q: dy 3y Vx +1+x = 0, y(0) =1 dx

A: Explained below

Q: Solve the IvP y'+aty%3D1

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Q: y = xy' – y* + 1 find general solution and particular solution.

A: Given, We have to find general and particular solution for it. Working:

Q: (1 point) Solve the following initial value problem: dy + 7y = 9t dt with y(1) = 9. %3D y =

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Q: y = In (x+ v5² +1) 3. Solve the y'" if x = 0.5 using step size of 0.1

A: We approximate the second order derivative using second order central difference approximation.!

Q: x’y" – 3xy' +3 y=3 ln x- 4 y(1)= 0 y'(1) = 1

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Q: y'

A: The function is given as : y'''-y''-2y'=0. To find the general solution of the function , The…

Q: Y = C1e* + C2ex + C3e2x where y(0) -D 0, y (0) %— 1, у"(0) — 2

A: The differential equation is: y=c1e-x+c2ex+c3e2x At x =0, y = 0, so c1+c2+c3=0....(1) At x = 0,…

Q: y' = 2x - 3y + 1, y(1) = 5; y(1.5)

A: y'=2x-3y+1, y1=5, h=0.1. We have to find y1.5.

Q: Q-1:B: Solve the initial value problem d?y + 4y = 8x2 ,y(0) = -3,y'(0) = 0 %3D %3D dx2

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Q: Solve y" – 6y' + 8y = 3e, where y(0) = 1 and y'(0) = 3. %3D

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Q: 3. Solve y'" + 6 y' + 9 y = 0, y(0) = 5, y'(0) = - 8 %3D %3D y (t)

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Q: 2. Solve the initial value problems using separation of variables. a. x' = t²x² , x(0) = 1 x(t) = t…

A: Given equation is dxdt=t2x2            (i) By using separation of variables,…

Q: Soru 1. (1+ 25)dx + 20* (1 - )dy = 0 ; -) dy = 0 ; + 2ey) dx y(0) = 1,

A: Given that:                           1+2exydx+2exy1-xydy=0    .........................(1)…

Q: 5 solve the 1UP: y% 4y(2)+ 3y'= Y1)=e+ % ,uG) = et %

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Q: Solve the initial value problem. dy ху?- сosrsinx а. у (0) %3D 2 dx (1- x?)

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Q: 3x 3 y' = 2y(y- 3).

A: Given differential equation is: 3x.3dydx=2y2-6y9xdydx=2y2-6y Apply variable separable form:…

Q: 7. Solve (a) y' = (5y²)-1

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