Express the solution of the given initial value problem in terms of a convolution integral y" + 10y' + 21y = cos(at); y(0) = 1, 7 y(t) 3 -7t e drX -3t +. cos(a t – a t) (e-37 – e-1") -- 4 4

Q: Find the solution of y" − 8y' + 16y = 0, y(0) = 1 and y'(0) = 5. y(t) = Ae4t + Be-4t y(t) = e4t+te4t…

A: The given equation is;  y''-8y'+16y=0, y(0)=1 and y'(0)=5. We have to find the solution of given…

Q: Find the general solution of (D²-7DD' + 12D'2)Z = sin(x - 2y) + ex-2y

A: This question is from linear partial differential equation.

Q: The solution of 1y"+ y' = 0, y (0) = 0, /(0) =1 /(0) = 1 %3D is y(a) = %3D (A) cos a (B) sin a (C)…

A: The solution of a differential equation must satisfy the differential equation. Check the options…

Q: Find c₁ and c₂ so that y = c₁ sin(2x) + c₂ cos(2x) is a solution of the BVP y" + 4y = 0, 0, y'(π) =…

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Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

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Q: Solve the D. E. to the I. V. P. sinx(e + 1)x'- cosx 1, y() = 0 O (1 + e') (1 + cos x) = 2 O (1 + e)…

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Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 4y = - 400 sin(2t) Y(t)…

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Q: (1+x2) y + 8xy' +6y=0

A: We have, This differential equation doesn't have a constant coefficient for the second derivative is…

Q: y" + + 3y¹ - 2y = sin ¹/2 x - x 3 y (0) = 1 ; y' (0) = 0

A: link used to solve system of linear equation…

Q: Solve: [xcos² (y/x) − y]dx + xdy = 0 4lnx + sin(2y/x) = C 2y 4lnx + sin(2y/x) = C x sin(2y/x) = C +…

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Q: Зу" — бу' + 6у%3D е' sec x

A: Given differential equation, 3y''-6y'+6y=exsecxy''-2y'+2y=13exsecx

Q: (D³ + 4D² + 9D + 10)y = -24e¯* when x = 0, y = 0,y' = -4, y" = -10 ANSWER: y =e-2* + e-cos (2x) -…

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Q: Find the general solution of y''' − y'' − y'+ y = 1 + sin x + sin 2x + ex

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Q: y" + 2y' + 2y = 5x² − 5 cos(2x); y(0) = 12, y'(0) = −2

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Q: Consider the D.E. y+4y" 1- cos(2r). Then a suitable form of the particular solution can be written…

A: A linear non-homogeneous ordinary differential equation with constant coefficient has the form…

Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

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Q: Q2: find the general solution: (D* - DD')z = (x² – 2y)e" + sin (2x – y) •2

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Q: 8. (y – In æ) dæ + (x +1) dy = 0, y(1) = 10 Ghenoral Form : y' + Pixly= Q(x) I (x): PLk) du : Final…

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Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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Q: y" – 4y' + 13y = e2x cos 3x -

A: Differential equations

Q: Solve. y" + 6y (v¹)³=0 a. v(x) = C₂e1*-6 C₁y+y³=C₂ + x b. C. (C₂-y)² + x² = C₁ d. y=C₂-In(C₁-x²) e.…

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Q: Solve the equation y" +4y= S(t-4π), y(0) = 1/2, y'(0)=0 a. )= = cos(2t) + sin(2(t − 4π)µ(t − 4π)

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Q: 2. Sketch the graph of F(r) on the unit interval, where F(z)4z(1 -z). Conclude that F, has at least…

A: Concept: The pictorial representation of data or values which are in an organized manner then it is…

Q: y" + 3y' + 2y = e* (t2 + 1) sin(2x) + 3e- cos x + 4e"

A: Answer

Q: Solve the nonhomogeneous equation using the method of undetermined coefficients: y +4y=x-2 cos 2x,…

A: The solution is given as

Q: Use undetermined coefficients to find the particular solution to y' + 4y' + 3y = = 260 sin(2t) Y(t)…

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Q: Find the general solution of y" + 12ly = 0. Oy(t)=c₁e-12¹+c₂e Oy(t)=c₁e¹¹+c₂e Oy(t) = c cos 11t+c…

A: This question is about ordinary differential equation.

Q: y" + 16y2x sin 4x

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Q: Find the general solution of y" - 8y = 4 cos (3x)

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Q: Solve. y" + 16y = u6(t). y(0) = y'(0) = 0 S f(t) for t 6 The solution can be written as y(t) Find…

A: In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace…

Q: Find the general solution of the x²y" + xy' − y = 3x, x‡0;

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…