Example 8: Find the solution of ÿ – 4ỷ – 12y = xe4* Sol: The chr. Eq. is r² – 4r – 12 = 0 (r – 6)(r + 2) = 0 → r, = 6,r, = -2 %3D y = c¿e"1* + c2e*2* yc = c,e6x + Cze¯2x %3D yp = (Ax + B)e4* ўр — Ае4х + 4(Ах + B)e4x ÿp = 4Ae4x + 4Ae*x + 16(Ax + B)e4x -12A=1, A=-1/10 , Jaleoxe4x 4A-12B=0, Jales e4* ,B=-1/36 ур — 36 e*(3x + 1)

Q: 4. Verify that rı = et + te' , x2 = et – te' is a solution to the given system: x = 2.x1 + x2 – et x…

A: Note: " Since you have asked multiple question . As per our guidelines we are supposed to solve only…

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Q: Consider the linear ODE 2°y(3) + 6x?y" + 4xy' – 4y = 0 -2 and In x are solutions to the ODE and…

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Q: Tim The solution of the nonhomogeneous DE x'y" - 2xy' + 2y = 2x + 2 is y=c;x+c,x? + 2x?+x² - 2x'lnx…

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Q: ! Consider the nonhomogeneous DE: y" + y' - 6y = (12 – 16x)e*. A) Verify that y, = 4xe* is a…

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Q: A fundamental set of solutions to y"+ 6y + 13 = 0 is y1 = e-* sin(2t), y2 = 3t sin(2t), y2 = e'…

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Q: ! Consider the nonhomogeneous DE: y" + y' – 6y = (12 – 16x)e*. - A) Verify that y, = 4xe* is a…

A: The given differential equation is y''+y'-6y =12-16xex. At first we have to verify yp=4xex is a…

Q: Example: solve y'=ty+1, yo = y(0) = 1, 0<t1, h=0.25 Solution: fis linear in y. So, solving the…

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Q: O vo) - 5y + 9y(4) + السؤال .8 The homogenous D. E. with constant coefficient of at least order…

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Q: 1. Given that { vin-() -() } 2e4t x (t) = e4t is a set of fundamental solutions for the homogeneous…

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Q: Consider the IVP given by o y" + 3y - 2y = sin(e); y(3) = 3, y/ (3) = 3. a) The solution of the IVP…

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Q: Consider the system of first order ODE a' (t) = Aæ(t) where Го A = 1 1 1 1 0 2 (a) Find the general…

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Q: 1. Consider the DE dy dz dy -5- + 4y = 8x + 2, y(0) = 1 dr Verify that y = Ae + 2x + 3 is a solution…

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Q: 2- Consider the approximate solutions of the form ũ, (x) = x(1 - x)(co + Cx) to the two-point…

A: The point collocation method is a useful method in solving boundary value problems. Unlike the power…

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A: The differential equation can be solved as follows:

Q: 1 Given, y = is a one-parameter family of solutions of the first-order DE y'+2xy = 0. 2 x´ +c Find a…

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Q: Find the particular solution to x2y'' - 3xy' + 68y = 0 that satisfies the initial conditions y(1) =…

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Q: 9. (a) Show that the functions r(t) = 3et+ 7e-t and y(t) = 3et+21e-t are solutions of the system I'…

A: Given: 9. a) x(t)=3et+7e-t and yt=3et+21e-t and a system, x'=2x-yy'=3x-2y satisfying the initial…

Q: 2. Use the method of undetermined coeffcients to find a particular solution of the system r = r2 - 5…

A: Answer

Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 2x + 3e…

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Q: Consider the linear ODE *'y() + 6a?y" + 4®y/ – 4y = 0 (a) Verify that y1 = *, 2 = -2 and y3 = -2 In…

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Q: 1. Find the steady-state solution y, to y" + 2y' + 16y = cos 3t and find the ICs y,(0) = Ypo, Yp(0)…

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Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 2x? +…

A: Using diffenrentiation

Q: 5. Consider the system: dx = x - y+ 3x - 2xy? dt dy -x+y+3y - 2x*y dt Show that the system has no…

A: Solution:-dxdt=x-y+3x3-2xy2dydt=-x+y+3y3-2x2ydxdtdydt=x-y+x3x2-2y2-x+y+y3y2-2x2Hence 0,0  is…

Q: 4. Consider the DE 3y' = (y – 1)(1 – 2y). (a) Which of the following is an explicit solution of the…

A: As per the company policy i can answer only first three subpart. More than that, leads me towards…

Q: Solve the IVP 22 + 1ox+1 %3D y Co) =0, y'(0) = -6 Osi ng the quasi-polynomial method.

A: y''-3y'-4y=0 D2-3D-4=0 D2 -4D+D-4=0 (D+1)(D-4)=0 D=-1,4 Complementary function =c1e-x +c2e4x

Q: Question 2: A) Verify that y = c₁e-x + c₂e5x is a solution of the DE: y" - 4y - 5y = 0. B) Find a…

A: Topic = Differential equation

Q: 1- y"+y'-2y = x² + e³x what is the particular (nonhomogenous) solution of the given ode? OA) Y =…

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Q: 1) Consider the DE x²y" – xy - 15y = 2x - 4 %3D | A) Verify that y = x and y2 = x x-3 satisfy the…

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Q: * السؤال .8 The homogenous D. E. with constant coefficient of at least order which has the solution…

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Q: 4. Consider the forced undamped system described by the initial value probler u" + 2u = 2 cos(wt),…

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Q: Find a particular solution satisfying the given initial condi- tions. 14. у3) — 6у" + 11y'- бу %3D…

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Q: Q1. Find the first approximation for the following nonlinear system using Newton-Raphson method with…

A: Given nonlinear system is 3x1-cosx2x3-12=0     (i)x12-81x2+0.12sinx3+1.06=0…

Q: t Consider the DE 'y" - zy' - 8y = 3z - A) Verify that y =and y =z satisfy the DE: z'y" - zy -8y =…

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Q: Use the method of variation of parameters to find a particular solution of the DE (3x – 1)y" – 9xy'…

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Q: The solution of the nonhomogeneous DE y" – 5y' +4y= 4x+3 is y=x-2 y= cje*+ c,e* + x- 2 y = c;e +…

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Q: Consider the homogeneous DE: y" - 2y-8y = 0. A) Verify that yı e1r is a solution of the given DE. B)…

A: Solve by second order differential equation.

Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 2x + 3e…

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Q: The Euler method for approximating a solution to the first order IVP: y' = 2? – y, y(1) = is Yn+1 =…

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Q: 2. Find the Wronskian for the given Y" +5Y +4Y = 0, Where two solutions are y, = e-4t , and y2 = e-t…

A: We use the definition

Q: Match the following guess for the method of undetermined coefficients with the second-order…

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Q: 5. Consider the system: dx = x - y+3x' - 2xy? dt dy =-x+y+3y' - 2x'y dt Show that the system has no…

A: The condition for no periodic solution is that the sum of the partial derivative of the first…

Q: is a one-parameter family of solutions of the first-order DE y' = y – y². Find a solution 1+c¸e¬* of…

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Q: The solution of ä – a = 0 with initial values r(0) = 1, y i(0) = uoi is given by: %3D Select one: O…

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