Obtain the general solution.  1. (D4 + 3D3 + 2D2) y=0  when x=0, y=0, y'=4, y"=-6, y'''=14 2. (D3 - 4D) y=0  when x=0, y=0, y'=0, y''=2 3. (D3 + 7D2 + 19D + 13) y=0  when x=0, y=0, y'=2, y''=-12

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Q: 2. Solve dx2 d²y for x = u? + 1 and y = 3u3 – 3u in terms of the parameter u. -

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Q: V Solve using variaton of parameters or recuction of order (D. 3D+ 2)y = (1+e*)

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Q: Find the General solution Use method of undetermined coefficients. 1. (D² l)y=ex (2sinx + 4cosx).…

A: To Find: the general solution using the method of undetermined coefficients   1. D2-1y=e-x2 sin(x)+4…

Q: В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2…

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A: Given Differential equation is D2+2D3+10D2y = 0

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A: →∫1a2 + x2dx  = 1atan-1xa→ddxuv = udvdx + vdudx

Q: Obtain the particular solution 1. (D³ +6D² + 12D + 8)y=0 when x = 0, y = 1, y'= -2, y" = 2 2. y" +…

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Q: Solve (D2 – 2)y =0 O a. y = cqevZx + c2e¬vZx O b.y= "(c,cos/2x+ c,sin/2x) O c.y = cqevZx+czxe¬VZx O…

A: The equation D2-2y=0 represent y''-2y=0 . Consider the solution of the differential equation is in…

Q: 6. Find a general solution to the third order equation y" + y" + 3y – 5y = 0.

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Q: Obtain the genral solution. (D³ +5D²+7D+3)y=0 y=eX(C₁-C₂x) + С3e-³x + С₂e-³x Oy=eX(C₁+C₂x)…

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Q: Q4: Find the general solution of d?y dy - 3 - 4y 3e2t + 2sin t - 8et cos 2t, dt dy y(0) = 2, (0) %3…

A: Given that  The differential equation  To find the general solution

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Q: d2y/dt2+5(dy/dt)+6y = t2+2t  Solve the equation using the method of change of parameters.

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Q: Q1. (4 marks) Find the general solution of the Cauchy-Euler equation: x²y" – 3ry + y = x°, r>0.

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Q: Solve for the particular solution: dy + 를y3D -2°y"; y(-1) %3D2 dz

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Q: b. Solve by using variable separation method. = 0 ax2' ay2 Which satisfies the conditions, u(0, y) =…

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Q: he equation ay"+ by' + cy = 0 has a unique solution satisfying y(0) = 1 and y'(1) = 2.

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Q: 8. Using the Runge-Kutta method of the fourth, solve y" = y + xy', y(0) = 1, y'(0) = 0 to find…

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Q: 6. Find the particular solution indicated. a. (D² – 2D – 3)y = 0; when x = 0,y = 0,y' = -4 Show…

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Q: 2. In each exercise, obtain the particular of solution. 2y-) dy = 0: when x= 0, y = 1 (3x +v) dy =…

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Q: Identify the Cauchy-Euler equation. O g- 52* + 8y = 0 dz4 22 y" – 7xy' + 6y = 0 O 2y" + 2a?y" – y' +…

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Q: (D³+3D²– 4D)y = 0 -4x Question 5 Find the solution. dy 31+9y=2ty 5/3 dt

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Q: -B-2-1 -2 -3- -8- 16+ hich equation best represents the linear functi Oy=-5x + % Dy= -5x+ 3 Dy= % x…

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