2. Solve the following equations. (). (a) sin? + cos? x = 1, where x E [0, 2ñ)

Q: 2:)y= 2x cos G) yous? (x²) +y sin² (x?) 2

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Q: 1. 6(x) = e- sin a, for y' + y cos x

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Q: 2. cos?x dx =x+ sin 2x + C X_SO

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Q: Solve the fllowing D.E +4y= cos x - sinx 2. CoS X %3D

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Q: Find the solution of the equation = e cos y dy? which tends to zero as x → 00 and has the value cos…

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Q: Solve the following equation using separation of variables: dy 2y- cos(x) dr 1+ sin(x)

A: Cross multiply the equation and solve

Q: Find the solution to the equation sin x - 1 = 0 on 0 s ¤ < 2

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Q: G- tanx) ydx + Inlexy cos x| dy = 0

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Q: Q1:- Solve the following DEs:- xy²-cos x sin x y' %D У(1-x2)

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Q: e n'rdr 17 cos'x Sin 2. 4

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Q: 4.2 Given g(x) = ) = cos z + sin for 0 <<, find the value of f(x + 1)dg(x). END

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Q: A particle travels along the x-axis such that its velocity is given by v(t) = (t25 + 4t) cos (3t).…

A: The velocity of the particle is given by: v(t)=(t2.5+4t)cos(3t)

Q: 3- the solution for the following O.D.E y' = In(x) + tan (x) %3D

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: A B 25/sin² 5 (sec 0 - cos 0) d )* Which of the following is equal to S; x² +25 dx ?

A: The given integral is x2/sqrt(x2+25).

Q: /2 (e) [™¹², sin(x) cos(x)dx

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Q: 15. For fe' cos x dx, what is du? cos x e' dx - sin x dx G(e* cos x + e" sin x) + C

A: The given question can be solved as shown in step2.

Q: 3. Eliminate the Arbitrary Constants (C, and C2) in the equation. (25 pts) y = C,cos (At) – C2 sin…

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Q: Solve the following equation on the interval 0se<2T. sin 20+ + cos 0 = 1- sin e

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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: a) y = cos(e 2x) (e2x) -1

A: Differentiate wrt x

Q: B-The result of dy/dx for the following function is cos x y = 1+sin x

A: We have to find out derivative

Q: 3. Solve for fe)(r) given that f(r)% = sinh(3r)

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Q: Compute S cos (x) sin²(x) dx

A: To solve the given integration problem ∫cos3(x).sin2(x) dx

Q: Solve the equation for x if 0 < r < 2n. 27. Cos a + sin e V2 Preview

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Q: B-The result of dy/dx for the following function is COS X y 1+sin x

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Q: 4. y= e (A cos x + B sin x),

A: Formation of differential equations: As a rule, one reqruires  n+1 relations to eliminate n…

Q: 2- Find the Root of the function F(x) = e*(3.2 sin(x) - 0.5 cos(x)) Using XL=3 , X,=4 , ɛs = 0.002

A: Let f(x)=e-x(3.2sin(x)-0.5cos(x))…

Q: b) Solve the following differential equatión . = 1 + Sin x + 4x dy +2y dx dx

A: According to the given information it is required to solve the differential equation:

Q: Q/ solve the differentil-equation ty-f'sinx-x)+(3xy+2y.cosx)

A: We will solve the problem.

Q: 4. Find the solution of the equation = e * cos y dy? which tends to zero as x → 0o and has the value…

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Q: 3. Solve the following equation by secant method, using the range (-1, 1). F(x) = 2 cos(x) –…

A: Lets solve the problem using secant method

Q: dy 2y =x'cos 3x dx

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Q: O Find the values x where fe) = t-2 24 cos(2t) has a local min fmax.

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Q: 2- Find the Root of the function F(x) = e*(3.2 sin(x) - 0.5 cos(x)) Using XL=3 , X,=4 , Ɛs= 0.002

A: This is to be solved by successive bisection method.

Q: 9. 3 cos(wt –@), where w and a are constants.

A: We use first Cos(a-b)=cos(a) cos(b)+sin(a)sin(b) and then we use Laplace transform of…

Q: Solve the following Riccati equation dy _2 cos? x – sin² x + y² 2 cos x y1(x) = sin x dx

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Q: Find the solution of the equation a²z a²z + Әх? ' дуг which tends to zero as x→∞ and has the value…

A: Given: The equation is ∂2z∂x2+∂2z∂y2=e-xcosy. Also, the given equation tends to 0 as x→0 and its…

Q: 6. S sin*(e³*) cos(e³*) e³× dx

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Q: .2n erl4h cos²0 r² dr sin@ d0 ¢ dộ = x 32πα 1 X = ? 0 JO

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Q: 1. Solve the following DEs and express your answers in explicit form. a) y' = -2x((y+1) b) sin rdy =…

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Q: 3. Calculate L {e=# cos(2t – 7)} COS

A: Given function is as below :

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

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

Q: dy cosh x dx + (sinh x)y = e-x

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: S 4 cos (x) sin (x) dx = %3D

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Q: Solve the following equation using separation of variables: cos(x) dy 2y d.r 1+ sin(x)

A: Solution of following equation using separation variable 2ydy/dx= cos(x) /(1+sin(x))

Q: Solve the following Bernoulli's equation by using an appropriate substitution. sin y (x + sin y)dx +…

A: We have to solve the give Bernoulli's equation by substitution.

Q: Solve the following equation on th e interval [0, 27]. cos x + 2 cos x+ 1 = 0

A: Given : cos2x+2cosx+1 = 0

Q: d?s sin 3t + cos 3t dt2

A: Explanation of the answer is as follows

Q: e* cos e* dx J 4 + sin²e* A 1 tan-1 2 sin e* + C sin? e* + C 2 2 tan-1 B sin e* tan- 2 1 tan-1 2…

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Q: 20. e2= cos(z/4) dz

A: