Let z1 = 2(cos() + i sin 12 and z2 = 6(cos() + i sin). Find z1z2 and (Enter your answers in a + bi form.) Z2 ZĄZ2 = Z1 %3D Z2

Q: 24 cos 4x – 32 sin 4x а. (с, + 4x) сos 4x + (c, + 3х) sin 4x b. c,e2x + C2e 3x + 3 sin x C. none of…

A: follow the next step

Q: -1x 54cos If cos -1 00, prove that b. a x² 2xy ,2 = sin C. COS a+ ab %3D 2

A: Introduction :

Q: 2 y = A cos 4x + B sin 4x +sin 3x b) 7

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Q: 5. Find the general solutions of the equations i) Zx - 4z,, – 5z, +10z, = cos(x+3y)-sin(x+3y) %3D

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

Q: 2) find the radius and coordinate center for the equation 2x42y+10y-12х-20-0 3) prove that sin 2x…

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Q: y" +3y' – 2y = e-2*[(20x + 4) cos 3.x + (-32.x + 26) sin 3.x] |

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

A: We need to find all the solutions of 1+sin (3x)=cos(0.25x), x∈[0,π].

Q: Given that Y1 = x-1/2 cos x and y2 = x-1/2 sin x from a fundamental set of solutions of (--)- x²y" +…

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Q: Use a CAS to find the solutions of y′ + y = ƒ(x) subject to the initial condition y(0) = 0, if ƒ(x)…

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Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0 |

A: We will find out the required solution.

Q: If 0 < 0< and z= (sin 0+i(1- cos 0)) find in its simplest form arg z.

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Q: 3. Find g'(x) if g(x) = sin³(4x) %3D A. cos (4x) B. 3 sin?(4x) cos(4x) c. 12 sin (4x) cos(4x) D. 4…

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Q: cos 3t dt 5 + 3 sin 3t Ocos 3t

A: Given- ∫cos3t dt5+3 sin3t We have to find u which is used in evaluating the given integral and to…

Q: 2. Vsin 3x cos 3xdx

A: Given: I=∫sin3xcos53xdx For evaluating given integral, we substitute sin3x=t…

Q: Solve the following 1 √√1-3x siny Cos 2y +1 cb₁ x² y² + x³ In x = 1 - 3 xy (a) - dx + dy = 0

A: We have to solve the differential equations given as follows a) 1sin ydx+1-3xcos 2y+1dy=0b)…

Q: Let z = 8(cos 50° + i sin 50°) and w=2(cos 30° + i sin 30°). Express in the form r(cos+ i sin 0):…

A: Here we can use the following formula to find the results eiθ=cos θ+i sinθande-iθ=cos θ-i sinθ

Q: 3 Find ALL solutions of cos 2x = 2 %3D

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Q: Q.3- Prove that: 2n 1 (cos =0 +i sin-) + 10 2cosne eino

A: The given problem is to prove the following complex identity. (cos n/5 θ +i sin 2n/10 θ)+1/einθ =…

Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, + 3i.…

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Q: 1. a. Let In = exp (nx) sin (exp (x)) dx. By making an appropriate substitution, or otherwise,…

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Q: 4. a. Show that for 0 Va² + sin² a. b. Generalize the result in part (a).

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Q: Show that the following equations have at least one solution in the give x cos x – 2x + 3x – 1 = 0,…

A: Given: To explain the given statement as follows, Here, the equation is  .

Q: The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) -…

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Q: 5. Find the general solution to the DE using the method of Undetermined Coetficients: y" + 9y = 2…

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Q: Q1: (1) Show that the value of € (-1, π), for which: sin² 0 1+ sin² 0 sin²0 1 + cos²0 cos² 0 cos²0 4…

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: 1 ao et/2 dt = 0.50 2 An e-1/2 cos 2nt dt = 0.504 1+ 16n? 8n b, = et/2 sin 2nt dt = 0.504

A: a0 = (1/π) ∫0π e-t/2 dt , put -t/2 = x , dt = - 2dx Using formula ∫ et dt = et + c a0 = (1/π) ∫ ex…

Q: V. Find the general solution of the following Bernoulli's Equation. 1. cosysin2xdx + (cos²y –…

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Q: 2) Find all solution of the equations in the interval [0,2x]. a) 2sin 30+ 12 = 0 b) (cosx- 1)(sin x…

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Q: When the general solution of y" + 4y = tan2x is written as y = U(x)cos2x + V(x)sin2x then which of…

A: The given differential equation is y''+4y=tan2x. The auxiliary equation of the corresponding…

Q: du Given u In[y cos(3x²y)1, solve CoS %3D ax

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Q: 11. Find the general solution of uyy - 4xu, = cos 2y – 2x sin 2y + 4x.

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Q: 4. Obtain all solutions of COS 2 = -i2 in C. Express your answers in the form r + iy where r, y E R.

A: Use exponential formula of cosz

Q: 21) (1 + cos 9t) 2 sin 9t dt

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Q: 1-Find the Cauchy principle value (showing details): J_co (7*+5x²+4)' cos(4x) dx 8.

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Q: . (a) Write cos 3x + i sin 3x = e3ix = (cos x + i sin x)³ by Euler's formula, expand, and equate…

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Q: 1. Solve the hyperbolic function of the following. i. cosh (-2 + j3) in the form of a + jb ii. sinh…

A: some formula  coshx+jy=coshxcosy+jsinhxsinysinhx+jy=sinhxcosy+jcoshxsiny i.…

Q: Determine the general solution of y' = cosx cos y

A: we have to find the general solution

Q: find a particular solution of y"-9y=-6 cos3x *

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Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

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Q: Find all solutions in [0, 2r) : 2cos (x) – sin (2x) = 0: 00, T 3n 2 4 4

A: We have to find solution

Q: -3 cos (2x)+sin(2x) in the form Rsin(2x+a)where R>0 and 0 <a<2n. Express

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: 3 Find all solutions of cos 2x for x if 0 < x < 2n. 2

A: The solution is :

Q: b. cos(3n) + 2 sin(3n)

A: Solution :-

Q: Let y= c1 cos 2x +c2 sin2x be a two-parameter family of solutions of the second-order DE y"+4y=0.…

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Q: c) Find all solutions of 2cos.xsin 2x - V3 cos x = 0. 5c.

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Q: z"- 4z'+5z = x sin3x- cos3x %3D

A: We first find the complementary solution  of the given differential equation by finding the roots of…

Q: Q2 Find all solution for cos(z) = 10

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Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

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Q: Show that, for any constants k' and 'a', u = sin(kx) sin(akt) is a solution of the equation Ut =…

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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.