(b) Solve y" +y - 6y = e2t.

Q: solve the initial-value problem x′ = Ax, x(0)=x0.

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Q: 2. Solve the initial value problem, D²ƒ – Dƒ = 0 f (0) = Df(0) = 1 with

A: Given  D2f-Df=0 with f(0)=Df(0)=1 The auxiliary equation is  m2-m=0 m(m-1)=0 m=0 or m-1=0 m=0, m=1…

Q: Solve using implicit differentation.    x ey = 3x-3y

A: Given;   x ey = 3x-3y

Q: Find a solution to the initial value problem, y" + 6x = 0, y(0) = -2, y (0) = -5.

A: y'' +6x=0⇒y'' =-6xIntegrating both sides,⇒y'=-3x2+c1Integrating both sides,⇒y=-x3+c1x+c2 We have…

Q: 2y Solve the initial-value problem ý+ = 4t, y(1) = 2. t

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Q: Solve the Bernoulli equation y' + xy = y4.

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Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

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Q: Solve the nonhomogeneous ODE. y" - 6y' + 9y =x²e5x

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Q: Find the solution satisfying the initial conditions: y" - y = x2 y(0) = 0 y'(0) = -1

A: Given that: y''-y=x2

Q: Q4: Solve the initial value problem: ty = 2y +t

A: Solution of initial value problem

Q: 2. Find the general solution of the first-order equation dy _ y² – 2ry dr

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Q: Solve the non-homo. D.E. 1.y" + y = 3e2x

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Q: the solution of the homogenous equation (хусот х -)dy - Ydx = o

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Q: Solve the second-order equation y" + 2y' – 3y = 9x with initial condition y(0) = 0, y' (0) = 0.

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Q: 5. Solve xdx + ydy а? (хdу-ydx) x2+y2 using exact D.E method.

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Q: Solve 1 . Find a particular solution to a' = x – y + e', y = -4x + y +t using undetermined…

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Q: x² – y Solve the initial value problem y' with y(2) = 4. %3D xy help (equations)

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Q: Q4: Solve the initial value problem: ty = 2y + t

A: Question. 4. The solution is,  y = y(t) = t³ + t²•C, where, C is the constant of integration.   The…

Q: y'e² 3-2х y' = y– xy

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Q: Use the method of undetermined coefficients to solve the initial value problem. y" + 4y = 1² + 4e¹',…

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Q: Use the Adam-Bashforth method of the second order to solve the second equation y’=y(x+y) when h=0.1…

A: Given differential equation is y'=y(x+y), step size h=0.1 with initial condition y(0)=1 Let x0=0,…

Q: Solve the initial value problem : y = 8x" -

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Q: Solve the first order equation (3r²y + 2ry)dz + (z³ + x² + 2y)dy = 0.

A: In the given question, the concept of the differential equation is applied. Differential Equation A…

Q: y" + 2y' = 121?

A: To find the general solution of a given non homogeneous differential equation first we will find…

Q: 3) Solve y"-4y't13y y0)=-l sy'co)= 2

A: The given differential equation is                                                     y''-4y'+13y=0…

Q: The general solution of the DE: -y = 1 is y= x(x + c)

A: given,1xy'-1x2y=1multiplying throughout by x we gety'-1xy=xnow, integrating factor μ(x) is given…

Q: Solve the initial value problem -39x + 120y, æ(0) = –39 y' = -12a + 37y, y(0) = –12. æ(t) %3D y(t):

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Q: 3. Solve y' = , with initial condition y(1) = 0. y2 – 1 x3

A: It is given that the differential equation dydx=y2-1x3. Using variable and separable method to…

Q: nd the general solution to: 2yy -e^ = 0, |

A: The question is taken from the calculus in which we have to find  the general solution of  given…

Q: Solve the initial value problem y' = 2ty", y(0) = Yo and determine how the interval in which the…

A: Initial value theorem

Q: 4 Solve y" – y" – y' + y = 2e¬t + te' + 3 by using both the method of undetermined coefficients and…

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Q: 2. Solve y' = 2x(x² – y), with initial condition y(0) = 1. -

A: This is first order linear differential equation

Q: Solve the stated initial-value problem. In addition, graph your solution and discuss its long-term…

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Q: What is the equilibrium solution of the equation y '(t) = 2y - 4? Is itstable or unstable?

A: The equation given is y't=2y-4. To find the equilibrium solution of the equation y't=2y-4.…

Q: 4. Solve the IVP y' = 2x-3y +e¯* y'= 2x- 3 y +e * with y(0) = 1 y(0)= 1

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Q: Q3) Solve the initial value problems: -V++ 2=0

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Q: Solve the initial value problem. d?y = 10 - 24x, y'(0) = 7, and y(0) = 5 dx2

A: Given d2ydx2=10-24x, y(0)=5 and y'(0)=7

Q: ) Find the general solution of the DE y = (2+y')x+ (y')².

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Q: y'+2y = te-2t , y(1) = 0  solve the initial value problem

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Q: Solve the initial value problem using y"+3y'+ 2y = 2u(t-2).y(0) = 0, y (0) = 0

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Q: Solve y' = 6x, x' = x + y with initial conditions x(0) = 1, y(0) = -2.

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Q: Solve the Bernoulli equation   y'-2.8y=-0.28y^2

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Q: Solve the initial value problem  y' = 3x2 -2y, y(0)=4

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Q: Find the general solution of the equation: e y' + y' – 2y = e - e |

A: As the given equation is a second order differential equation, thus write it in the general form and…

Q: Solve the initial value problem, y' = 2x y(2) = 0. 1+2y

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Q: (24) Solve : (n²y = 2xy²) dn. - (n²³-3n² y) dy zo

A: Solution

Q: 4. Solve y"- 4y' +3y = 1 by variation of parameters. %3D 1+e-*

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Q: O2: Solve the Second Order Non-homogeneous Linear Equation y" + 2y' +y = x²

A: The given second order non-homogeneous linear equation is,y''+2y'+y=x2

Q: Use two iterations of N-R method to solve the nonlinear equation with estimated solution xo = 2. V1+…

A: Given

Q: 2. Solve the IVP: *+ 2y = te-2", y(1) = 0 dt

A: