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: 7. (y + y cos x - ye*) dx + (3x + 3 sin x – 3e*) dy = 0; y (0) = – 1

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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: y(7) −4y(6) −4y(5) + 56y(4) −156y(3) + 224y'' −176y' + 64y = ex cos(x)−3e2x + xe−4x What is the…

A: y(7) −4y(6) −4y(5) + 56y(4) −156y(3) + 224y'' −176y' + 64y = ex cos(x)−3e2x + xe−4x

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: 1. Find dy/dx a) y = In (2x² – 3x) %3D b) y = [e" dt ) d) y = In|sec(x)+ tan(x) e) y = 7std*) S)y =…

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Q: 8. f(x) = 2sin² 3x a. 12cos(3x)sin(3x) b. -12cos(3x)sin(3x) c. 12sin(9x)cos(3x) 9. f(x) = 3 cos² a.…

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Q: Solve the separable I.V.P y' = (x2 + 4)(y² + 4), y(0) = 0. A. y = 2 tan[ 12x + 3x?] B. y = 2 tan[…

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Q: 4. Calculate zu for z = 2x-y x+3y x = e2u cos(3v), y = e2usin(3v) "

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Q: It is estimated that 60% of emails are spam emails. Some software has been applied to filter these…

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

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: Solve the separable I.V.P y' = (x² + 4)(y² + 4), y(0) = 0. A. y = 2 tan[ 12x + 3x2] B. y = 2 tan[…

A: Topic- differential equations

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

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Q: k. y = ln x 1. m. y = y = 5 cos x + 8 lnx + 3x³ 3x¹+3x²+1 x

A: Given: y= ln(x)Solution: y= ln(x)Differentiating y with respect to x we have dydx= ddx(ln(x)) ⇒y′=1x

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Q: y=(b+x²)* +(1+x°)* ( \3x² +x – c )cos²(4x) y'=? %3D %3D

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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: . (D²+1)y= 10e²x When x = 0, y = 0, y' = 0

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Q: Solve the following nonhomogeneous ODES. (a) y" = -4y + e2#; (b) y" – 4y + 3y = e²; (C) y" = y+ e²…

A: Given that  The following differential equation  To find the general solutions

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

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

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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: Solve for the general solution * (eУ — усos ху) dx + (2xe-У — х соs ху +2у) dy %3D0

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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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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…

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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.