. Obtain in two ways the general solution of (r+ sine – cose ) dr+r(sine + cose ) de = 0

Q: Given z = (e-2) (siny), find dr -2x O-2 e 2² (cos y) O-2 e 2 (sin y) O-2 e 2 (sin y) +e-2 (cos y)…

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Q: Evaluate by any applicable method. dx 0 x4+1 None of the choices. Please refer to my solution. O…

A: We have to find solution of given integral.

Q: Which of the following CANNOT be solved by method of undetermined coefficients? A (D2-3D+2)y=sin x+…

A: Given that:

Q: 1. Evaluate COS dır V1- 2 sin æ (7/6 (a) ( - z)e* dz (b)

A: To evaluate the given definite integrals.

Q: 6. Find h' (÷) , h" (), and h" (G), given h(r) = sin r cos 3r.

A: since you have asked multiple questions in a single request so we will be answering only first…

Q: Find an antiderivative of the given function. 4 cos 9x O A. sin 9x O B. - 36sin 9x O C. sin 9x O D.…

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Q: The integral (cos(3x))sin(3x)dr under the change of variable u = cos3r becomes ưdu. 9/29 Select one:…

A: Given integral:

Q: Show that there is exactly one solution f E L'([0, 1]) of the equation f(x) = 7 + sin(x) %3D

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Q: Solve (by separation of variables) the following problem du = 0 ; x E R , t> 0, t > 0, - и(х,0) =…

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Q: Find L {(2 – t) (5 cos 3t – 1)}.

A: Given that: L{(2-t)(5cos3t-1)}

Q: (D² - 2D+5)y=e* cos x

A: I am attaching image so that you understand each and every step.

Q: 2. Determine the general solution of this equation in terms of C r(1–0²) dr – (Br² – cos0 sin®)d@ =…

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Q: Determine the values of A, B and C. 2 X²V4 – x²dx = A sin? t cos²t dt B

A: Consider the integration as I=∫02x24-x2dx Put  x= 2 sint⇒2 cos t dt =dx Also  x→0⇒t→0Againx→2⇒t→π2

Q: S₁ + Sa cos²0 de 01/2000 sin ²0 de csc ³0 de + Sc 01/se sec ³0 de The integral dx (x²+4)² can be…

A: We have to solve above integral

Q: O Find the equatisns if ou know The rootsa Dy=Ge -4X +Cze %3D 2X LG cos 3X t (z Sin3X %3D -3X

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Q: Use the substitution formula to evaluate the integral. (1 + cos 3t) 2 sin 5t dt 15 15

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Q: T/4 cos(8) 5r* sin(0) dr de

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Q: Q/ Solve the DEs: 3-(cos x)y =y°0-1) sin x.

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Q: (sec(In x) y ху" + у' +:

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Q: The cos'ydy is equal to 3 A. siny + sin?y +sin³y - sin'y+ C sin'y + C 3 1 B. siny – sin³y + siny -;…

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Q: Obtain the general solution of the following: 2. -z (2- 2) sec'e 3. xdx + sin () Lydx - xdy]

A: 2. The given equation is  dθdz=z(z-z2)sec2θ This can be written as…

Q: V3 14) Give a general formula for all the solutions of cos 0 %3D

A: Given: cosθ=32

Q: the solving for equa tion ty=o is 1-y= COSX %3D 2-y= Sin x %3D y= tax

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Q: Q4) Find the complete solution of the following equations: a) y" +3y' = sin x + 2 cos x (15)

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

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Q: (c) The displacement, x, of a particle in simple harmonic motion is given by x = cos(3t) – sin(3t).…

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Q: 6. Find the solution to the following IVP. (a) r- 2y = x sin (2r) – r³ + 4t, given y(n) = . %3D

A: Given equation: xdydx-2y=x5sin(2x)-x3+4x4 Condition yπ=3π42.

Q: 1+e² sin z + z cos z

A: Introduction :

Q: Find all the four square roots of cos(0) +e¡ɛ2 sin(0). Hint: e¡e2e3

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Q: 41 cos t dt = 1+ sin?t /2 If q sec e de, then a = b = and q =

A: Solve the integral in the following way:-

Q: Find the highest point on the cardioid r = 1+ cos 0.

A: We cal solve the problem by doing the derivative and set it to zero for finding theta.

Q: Solve the Bernoulli's equation given below: dy -ycot 2x dx 3 CSC 2x ( )」 Sn 2メ= ーメキC a. C-2) Sin 2x…

A: We have to solve the Bernoulli's equation  By convert Bernoulli's equation in First order linear…

Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

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Q: Find dr/dθ in sin (rθ) = 1/2

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Q: Determine the roots of the following general equation. 1. y = Ce2x + C2e3x 2. y = (C, + C2x)e¬* 3. y…

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Q: V3 %3D 7) Give a general formula for all the solutions of cos 0

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Q: 2 (cos Fe tisin) - fsih 똥) Q) put Vz (cos 3+P sin I) 6. in expoitial hor m

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Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: (2{co(;)+ sin(;)})" Simpli fy, z = 1+v3i 0 22품 0 22플 O 42 O 24-

A: We have to simplify

Q: Q3. Calculate L{e-ª cos(2t – 1)} COS

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Q: -y'-Tany = x" (n # 0) 1 Cos?y

A: We change it into first order linear equation and then solve.

Q: The cos'ydy is equal to 3 1 A. siny + sin³y + sin³y -; sin'y + C 5 3 B. siny – sin³y +sinsy -sin?y +…

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Q: Find the first two positive solutions to 2 cos(t) t =

A: Trigonometric equation: - Trigonometric functions are used as variables in trigonometric equations.…

Q: The solution of the following Bernoulli's equation xy' + 2y = x¹(cos x) y² is

A: The correct answer is not given in options.The solution with the correct answer is given as

Q: Use imaginary part of the solution to the complexified version of the following ODE to find its…

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Q: Find y'. а. уе* 3D х сos y b. In(3y) %3D 2х + Зу?

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Q: А. Find the general solution of the following first-order ODE ху' — у + 2х3 sin? (2)

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Q: 4. (a) 5e-2' cos 3t (b) 4e-5t sin t

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Q: 4) The Integral cos'x dx ******* (a) : (b) 8 (c) (d) o 4

A: From the given problem:   I=∫0π2 cos2xdx...(1)   From the trigonometric relation:…

Q: The integral . (cos(3x))'sin(3x)dr under the change of variable u = cos3r becomes v u'du. 9/29

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