Consider the following IVP: у" + у'%3D -сos x; у(0) %3D а, у'(0) 3b Find the general solution. 1 1 y(x) = c,e-2" + cze * A - cosx + – - sinx 2 2 B y (x) = c,+c,e¯+ -coshx – – sinhx 2 2 1 y (x) = c,+c,e¯+-cosx – – sinx 2 C -2x D y(x) = c,e*+c,e-+cosx - -- sinx 2 D

Q: Find the solution of y" + 9y' = 162 sin(9t) + 1296 cos(9t) %3D with y(0) = 5 and y' (0) = 9. %3D y =

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Q: Solve the given IVP: (a) y""+y" - 2y' = 4e-²x/cosx; y(0) = 0.4, y'(0) = −0.4, y″(0) = -0.4

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Q: y" + 2y' = 4x – 5 cos(x).

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Q: Find the general solution:

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Q: Give a particular solution for y"– 2y' + y = ; ex 1+x2

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Q: Find a general solution of y'" = (- 50 – 50 i /3) y. ... y(x) = C, e +c2 e-

A: The given differential equation is y''=-50-50i3y Demoiver's theorem for fractional power  If rcos…

Q: y" (t) - y(t) = 4 cos(t) ;y(0) +0 , y'(0)=1.

A: The objective of the question is to solve the given second order differential equation with the…

Q: 3-(cos x)y' =yCv-1) sin x.

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Q: y" + 2y' = 2 – 5 cos(x), y(0) = 0, y' (0) = 1. %3D

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Q: By finding suitable integrating factors, solve the following equations: (a) (1-x?)y' + 2xy…

A: (a) Consider the given equation as equation (1) and obtain the integrating factor as follows.

Q: cos² xy' = (1 + y²)

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Q: Verify that y = c is (1+ce') (1– ce') is a solution to y' = + (v² – 1) , where some constant.

A: For verifying given thing, we find solution of given differential equation Now, for finding solution…

Q: (e) Find y' and y" for y = sin (x+y). %3D (f) Find y' for sin x+ sin y = 1. %3D (g) Find y' for x…

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Q: b. (1+y²)y" + xy' - 3y = cos x solve and show that this equation is non- linear and non-homogeneous.…

A: As per the question we have to use the solution of the given second order differential equation to…

Q: For cos2(xy) =, evaluate y' when x = 4

A: Given that: cos2(xy)=14

Q: y'+y = cos(e*

A: Given equation is: y'+y=cosex

Q: y" + y = cos x ; when x = 0, y = 0, y' =

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

Q: Find the general solution:

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Q: y" + 9y = e²* sin(x)

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Q: x2 sin3(x) Find ax if y = In \cos(x*).V1+x,

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Q: Determine the most appropriate method to find the general solution for the functions: y" - y' - 2y =…

A: Given differential equation is y''−y'−2y=2x+sin2x−4hcos2x. We have to determine the most appropriate…

Q: Q2/ If the following eq. is exact, then solve it (y cos x + 2xe") + (sin x+ x²e° + 2)y' = 0.

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Q: y" – y' – 2y = sin 3t y(0) = 1 and y'(0) = -1

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Q: Give a particular solution for y" - 2y' + y = 3e".

A: Explanation of the answer is as follows

Q: Find the general solution: 2y" + 3y' +y = 2e2 + x² + 3 sin(x).

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Q: y =V2 e-c is a solution of y' y sinx. -Cosx Select one: O True False

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Q: (1+x)y' + y = cosx; y(0) = 1

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Q: IV. y-y=sin x+cos 2x +e

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Q: xy2-cos x sin x y' = ху?-со -cOs x sin У(1-x?)

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Q: i- y' + 2y 4 cos 2x. yT) = 3 (using Bernoulli Equation) %3D %3D

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Q: (d) If x y/1-y², find

A: Solving question1 for other question repost.