Show that the following equations either are exact or can be made exact, and solve them: 2,,2 (b) 2xy' 3x y 0; (c) (cos2x +y sin 2x)y'+y0 sin 2x) v'

Q: for the equation 8x(x−1) +cos(x) =0 does the intermediate value theorem show at least one solution…

A: Let, f(x)=8x(x−1) +cos(x) 8x(x−1) and cos(x) both are continuous for all real values of x. So, f(x)…

Q: у" — 7у' 3D (2х — 1) sin 2 x -

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Q: 4sin 5x cos 3x-4cos 5x sin 3x/rom x= 0 to x= 2m

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Q: Find the solutions of the equation that are in the interval [0, 2π).

A: Known fact: sinA+B=sinA cosB+cosA sinB

Q: 4. Find the general solution of the equation: cosr– sin 2x =0

A: Use general solution

Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

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Q: Prove that the equation 5x − 7 − sin 3x = 0 has exactly one real solution, then determine an…

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Q: Evaluate sin (44°) + cos (29°) using differentials. Refer to special triangles.

A: To evaluate sin44°+cos29∘ using differentials.

Q: express sin 0 and cos 0 in terms of t. 2 6. By using t = tan Hence,

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find all solutions of the equation in the interval [0, 2x], correct to five decimal places. 5 sin 2x…

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Q: Find the solution of sin² (x) – 4sin (x) – 1 = 0 for all angles between 0 and 2n.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find the solutions of the equation that are in the interval [0, 2π).

A: the given equation is: sin2u=sinu we have to find the solutions of the given equation in the…

Q: 5. Find all solutions to 1+ sin sin 3x = cos cos (0.25x) such that xE[0,r]

A: The best way to do this is to use some numerical method to solve this. It is not feasible…

Q: is a root of the equation y2 + ycot x cos x - 1 = 0

A: Here we have to show that, y = sin x is a root of the equation y2 + ycot x cos x - 1 = 0

Q: of cos 2 2 sin 0) de has the form 1 -F 4 sin lue of 0 to make F(0) =0?

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Q: i) Find sin 6x+ cos 4x dx. 3 ii) Evaluate || et -dx . Hence, solve 2e* dx . (* +2)" +2

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Q: . Solve for x: 2 cos x + sin x = 2, 0<x < 27.

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Q: 2. y = 3e* cos 4x + 15e* sin 4x %3D

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Q: Solve che DE'sin with Euler 2?

A: For the solution follow the next steps.

Q: If cos(0) 1 and 0 satisfies T < 0 < , find sin(0). 2 - sin(0) = %3D

A: Given: cos θ=-16 &amp; π&lt; θ&lt;3π2 To determine: sin θ

Q: For cos x cos 3x – sin x sin 3x = 0, use an addition or subtraction formula to simplify the equation…

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Q: (2.) (1-(In))^ (3.) yn + sin ()

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Q: Find the first and second derivatives of r = [3 cos 2t, 3 sin 2t , 4t].

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Q: Find the solutions of the equation that are in the interval [0, 2π).

A: Known fact: cosC+cosD=2cosC+D2 cosC-D2.

Q: Find cos(4x) sin(4x) da.. To cos(4x) sin(4x) dx : =

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Q: (2 cos 2x+ 3 sin 2.x) 7. evaluated at x = 1 rad

A: Given query is to find the value of the expression at x = 1.

Q: (1 + cos 7t) 2 sin 7t dt

A: Here we use u-subsitution to evaluate the integral. d(cosx)dx= -sinx

Q: Find all solutions of cos^2(x)+cot(x)sin(x)=0

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Q: Given the integral sec6 (x − 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: The given integral,       ∫sec6x-1tan4x-1dx

Q: Find all exact solutions on [0,2x) of the equation cos 2t = sint +1

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Q: Verify y = 4 cos(2x) + 6 sin(2x) is a solution to y" = -4y.

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Q: Find sin 2x, cos 2x, and tan2.x if sinx= -- 3 and x terminates in quadrant IV. V13 sin 2x cos 2x tan…

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Q: 1. . Use the method of characteristics to solve the first order equation Uz – 2uy with u(x, x) =…

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Q: 3. Determine a root of the equation sin(x) + 3 cos(x)-2-0 Using the Secant method correct to five…

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Q: Solve: sin 3r dr + 2y cos 3r dy = 0 %3D

A: First make the differential equation in seperable variable form, that is taking function of x with…

Q: Find the exact solutions of the given equation in the interval [0,27). sin 2x = CoSx

A: Given equation is

Q: y = 3e* cos 4x + 15e* sin 4x -X -X- %3D

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Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

Q: 1=[", 64 cos(nx) dx x* -16 -08-

A: We have given integral, I=∫-∞∞64cos(πx)dxx4-16 We need to solve that integral.

Q: (9) Verify that Yp = sin 2x is a solution of y"– y = -5 sin 2r and use it to find the general…

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Q: COS X dx 1-sin x

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Q: V3 f. sin(2x) 2 tan(x) = 1

A: Solve the problem within the domain first find the inverse and then solve.

Q: 4 sin' 2x cos 4x dx 4.

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Q: y" + y = 3x sin x

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Q: b) Use the hyperbolic identity cosh(2x) = 2 cosh? (x)–1 to solve 4 cosh(2x)- 22 cosh(x)+19 = 0.

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Q: (9) Verify that yp = sin 2x is a solution of y" – y = -5 sin 2x and use it to find the general…

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Q: By using the method of undetermined coefficients, obtain the general solution for у" - 2y' - Зу %3 2…

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