Calculate Cos(y(2.500)) if y(x) is the solution of y" + 6y' + 9y = 13sin(2x) such that y(0) = y'(0) = 0. 0.694 0.906 0.541 O 0.146 -0.996 -0.703 0.506

Q: Let α(x) = ex2 . Verify the identity (α(x)y)' = α(x)(y' + 2xy) and explain how it is used to find…

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Q: A particular solution of y"-y'-6y=2sin(3x) cos(3x)-5sin(3x) -cos(3x)-3sin(3x) a. b. 8 13 C.…

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Q: Solve the following initial-value problem: y'+ (tan x)y=cos²x; y(0) = − 1 - O y=−(sinx)(sin x−1)-co…

A: We will find the required.

Q: cos(x)y' + sin(x)y = 2cos³(x) sin(x) — 1, y(4) = 3√2, 0 < x < 1/17.

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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: 6. Solve y sin (x) cos (x) with initial condition y'(7) = 1 and y(7) = 0.

A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

Q: A particular solution of x²y" + xy' + (x? – 0.25)y = 3x3/2sinx, x>0, y,(x)=x-1/2sinx, y2(x)=x1/2…

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: uestion/ a,. Use the define to wnite the fe Co 1)

A: I think 3rd no series is not  written properly.  Solutions for others two,

Q: Which of the following functions is a solution of x²y" + 5xy' -21y = 0. (а) у(х) — sinx (b) y(x) =…

A: here option c is true

Q: y""+y" = 3x² + sin x − 2 cos x -

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Q: (D² + D)y = 81r² +14 cos(4x) where y(0) = 0 and y'(0) = 3 %3D

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Q: Given that y(x)= sin( In 2x ). Which of the following formula is CORRECT to find y'(x). v(e) = (In…

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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 following. x' = 4x + y y' = −2x + 2y,   X(0) = (−1, 2) The general solution is (x(t),…

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Q: 2. Draw the graph z = - cos(y) for 0 < y < 2n, and then use it to help you sketch solutions of y' =…

A: Firstly we draw the graph of z=-cos(y) for the given interval. Then we find the critical points and…

Q: 10. If cos(x + y) = 2x- 2y, find y'.

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Q: Use undetermined coefficients to find the general solution of the ode 3 y" + y − 3y = cos(x) + 5x²

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Q: 8 cos(x) y=x

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Q: If y(v) = 10 COS 79 72 dr then

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Q: #17 Determine the equations of function graphed below.

A: According to question We have to calculate the equation of the graph.

Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

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Q: Solve cos(2x) = v3 cos(x) – 1 where x E COS [-27, 27].

A: Given x∈[-2π, 2π]

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: 2. Find the general solution. y' + sec x y = cos x. а. b. y' +y =÷(e* -e-*).

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Q: (b) _x²y″ − 2xy' + (x²+2)y = 0, given solution y₁ = x sin x -

A: (b) The differential equation is given as , x2y''-2xy'+x2+2y=0              .....1

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.