Use variation of parameters to solve the given system sin 2t x² = (2-1)x - (₂002)¹ X' (4 + Je4t cos 2t x(t) = c₁ [cos (2t),2 sin ( 2t) ] et + c₂[sin(2t), — 2 cos (2t)] + e[cos (2t), 2 sin(2t)]

Q: (b) у" — 2у + у 3 еt sin(z)

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Q: Give all the possible elementary divisors of a group of order 40.

A: 40=23×5 So, the possible elementary divisors of the group are 2,2,2,5,2,4,5 and 8,5

Q: Find the particular solution : y" + y" +4y sin2x sin2x (b) Yp =sin2x (a) yp = - (c) Yp =- cos2x ()…

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Q: The solution of (e +2ay) daæ + (2 cos 2y+ 2x?y) dy is given by (A) e" + a?y² + cos 2y = c (B) e +…

A: The given equation is; (ex + 2xy2) dx + (2cos2y + 2x2y)

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 general solution of y" + y = e + 5e2* is y = ei (A cos (*) + B sin )) + Ce-" + 응e2x 2 () V5z y =…

A: Given that  y"'+y=e^(-x)+5e^(2x) To find the general solution

Q: Find the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A…

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

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA…

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Q: Jx"(x* +2)"³ dx

A: We will find out the required value.

Q: Verify if y = c, sin 3x + c2 cos 3x + 9x2 - 2 is a solution to y' +9y = 81a?. Show your solutions…

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Q: dx 4. -' (x- 3)*

A: Solution is given below

Q: If x'y" +xy' + (x2 - -0 x>0 , V1=X 2 sinx and y=y,v. Which of the following equations satisfied by v…

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Q: The equation ? + sin(xy) + C = 0 is the general solution of O y' + cos (xy) = 2 (x + y) 2 (ydx +…

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Q: Using variation of parameters, solve the nonhomogeneous system X'= AX + g, where 1 A=[24] g=g(t) =…

A: Given that the nonhomogeneous system                      X'=AX+g, where                A=21-5-2,…

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA.…

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Q: Verify that (e* sin y-2ysin x)+(e* cos y+2 cos x)y' 0is exact. Then solve it and leave the answer in…

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Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: Find the solution of with y(0) 3 and y' (0) = 8. y = y" + 3y = 108 sin(3t) + 36 cos(3t)

A: see below the answer and explanation

Q: (b) y" – 2y' + 5y = eª cos 2x, y(0) = 2, y' (0) = –1.

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Q: Solve y' = cos(2x + y – 5) – 2. = COS

A: The solution is given as

Q: 1 = x²y" + xy' + cx? - +»v=o x>0 ,V1=X sinx , and y =y,v. Which of the following quations satisfied…

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Q: Find the general solution of (2x + y cos (xy))dx + x cos (xy) dy= 0 Show your solutions on a…

A: Solution

Q: Find the solution. y'= 1 + 3ytanx (A) 3y tan³x=c+ 3sinx-cos³x B 3y cos³x=c+3sinx - sin ³x D 3y…

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Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: Solve the equation y' + a = eax +)csc(ax+y), where a is a real number Select one: a. e-(x…

A: The differential equation is given as y'+a = e(ax+y)csc(ax+y)                          (1) Let ax+y…

Q: [(cos 2y) – 3x?y²] dx + [(cos 2y) – 2x(sin 2y) – 2x³y] dy = 0 %3D

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Q: x - ; )* ( sin 2t X' |X + 4 2 \2 cos 2t)

A: We have to solve the system of equations.

Q: . Using Bisection Method solve for the oot of f(x) = e¯x(x² + 5x + 2) + 1, [-1,0]

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Q: 8 cos5(α)/(sin(α))1/2 dα

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Q: Chosse the correct answer. A particular solution of x'' + x' - 2x = 2sin2t is given by: Xp(t) =…

A: Given non-homogeneous differential equation x''+x'-2x=2sin2t    ...(1). We have to find the…

Q: Solve cos(2x) + cos(x) = -1

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Q: y(5)_y(3) = e²+2x²-5 y(4) + 5y" + 4y = sinx + cos2x

A: Given: The equations are y5-y3=e2+2x2-5 and y4+5y''+4y=sin x+ cos 2x. The objective is to find the…

Q: Find the solution of with y(0) = 9 and y'(0) = 7. Y y" + 3y = 126 sin(3t) + 162 cos(3t)

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