Solve the following initial value problems: 1. y" - y' - 20y = 0; y(0) = -3, y'(0) = 3 2. y" + 8y' + 25y = 0; y(0) = 1, y'(0) = -1

Q: 3. y=√√2x (x²-2), y'=?

A: We have to find the derivatives.

Q: 5) Find the general solution of the following equation y" +8 y"-9 y=0

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Q: Solve the following IVP y"-y'+y/4=0, y(0)=2, y'(0)=1/3

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Q: Solve the following IVP. y"'-5y"-22y'+56y=0 y(0)=1 y'(0)=-2 y''(0)=-4

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Q: y'' = 2y' - 5y         y(0)=pi, y'(pi/4)=0

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Q: 8.) y" +2y' +5y = 3e 2* ; and y(0) = y'(0) = 1

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Q: Solve the following initial value problem y''+25y=5x,  y(0)=1 , y'(0)=5

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Q: Solve for y(x):  y’’ – 5y’ + 12y = 0; y(2) = 0; y’(2) = -4

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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: (3x - 1)y" (3x + 2)y' (6x8)y = 0, y(0) = 2, y'(0) = 3; y₁ = e²x

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Q: 5. Solve 3y" (x) + 2y'(x) - 8y(x) = 0, y(0) = 6, y'(0) = 18

A: 3y''x+2y'x-8yx=0y0=6y'0=18

Q: y(4) - 4y" + 6y" - 4y+y=0; y(0) = 0, y'(0) = 1, y'(0) = 0, y" (0) = 1

A: The Laplace transform is used to find the solution of the linear ordinary differential equation with…

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: 4 y'+− y = 2; y(1) = −4 {y= X 2 = 5 -x-- 22 X 5

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Q: x²y"-9y" + 6y' - 9 = x² + 6x y'(0) = 0

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Q: 6. Solve the IVP with y(1) = 2 and ty' = 4t² - 2y.

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Q: Solve the following initial value problems: (y + 2y - 3y = u(t-1)-u(t-3), y (0) = 0, y'(0) = -1.

A: The initial value problem is given as y''+2y'-3y=u(t-1)-u(t-3) with initial condition y(0)=0,…

Q: Given equation is using Laplace 1- y" - 3y' + 2y = 4e²t y(0)= -3 & v'(0)= -5

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Q: 1. y' = 2(3x + y)? – 1; y(0) = 1

A: Given that: y'=2(3x+y)-1, y(0)=1

Q: Find y' y= y" = 3x + 4 2x-3

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 0. Solve y"+8y'+20y = 0, with y(0) = 2, y '(0) = -7.0

A: We have to find the solution of given differential equation.         y’’+8y’+20y=0  ; y(0)=2,…

Q: f y=y(x) is the desired solution of 2 = f(x,y), Derive Euler %3D teration formula for solving ODES…

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Q: Solve the initial value problem: 16x" 24x' + 9x - = 2t 2e3, x(0) = 0, x'(0) = 10

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Q: Solve the initial value problem y' = 6y5 with y(0) = 3. y(x) = f(x), with f(x) = 3 To input, say,…

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Q: Solve (D-2)²(D²+1) y=0,y (0)=1y '(0)=2, y'' (0)=3, y''' (0)=4

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Q: 2.3 - y 5e2, with y(0) = 0 and y'(0) = 1 %3D

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Q: Solve the following IVP y' = e(2x - 4) y(5) = 0 O ev = x² - x - 4 2 2 ey = x² - 4x − 4 T ex = y² -…

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Q: 5. Solve the equation y-y'y"=1, given that y=√2 and y'- and y'= when r=0.

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