Solve the D. E. to the I. V. P. sinx(e + 1)x' – cosx = 1, y(0) = 0 COSX O In (1 + cos x) = 1 + e (1 – e) (1 + cos x) = 40 (1 + e) (1 + cos x) = 4 (1+ e) (1 - cos x) = 1 %3D O (1 + cos i) = 1+ e (1-e)(1+ cos x)= 2

Q: What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD.…

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Q: Find ay dt + = -1 (+-√e ³ sin ¹ (2+) 1(5+2log +) 9

A: We will use the formula ddtmn=nm'-mn'n2

Q: and if f(x) = sin" (x²) Lim 0 find 2m + n f(x) f'(x) (1 − cos x)m - = 2√√√3

A: Given that                                                            Formula:…

Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

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Q: Solve the D. E. to the I. V. P. sinx(e + 1)x'- cosx 1, y() = 0 O (1 + e') (1 + cos x) = 2 O (1 + e)…

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Q: If x'y" +xy' + (x2 - -0 x>0 , V1=X 2 sinx and y=y,v. Which of the following equations satisfied by v…

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Q: y= sin(x + 4) cos (x - 4) y= sec 4x + tan 4x y= Arctan

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: ; Choose the most appropriate answer. (i) Let 1-r 2 E (an cos(ntx) + bn sin(nrx)], n=1 on (-1,1).…

A: This is Fourier series expansion of (1-x) from -1 to 1.

Q: Calculate ㅠ 2 6³ cos² (4x) sin² (4x) dx

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Q: The general solution of dy/dx-2/x y=(y/x)^3 sin [x] is y^(-2)=1/x^4 (2x cos [x-2 sin [x+c)] O A.…

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Q: dt cos (2 sin 21) /1– 4r

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Q: One approach to evaluating 2 cos (2x)dx is to first rewrite it as cos(4x) + 1 dx а. cos(2x) – 1 dx…

A: This is the question of integration.

Q: العنوان solve b sin ² (3x) cos² (5x) dx 2 8 tan³x dx >

A: First, we need to identify the type of integral we are dealing with. The first integral is a product…

Q: Find f. f"(x) = 5 + cos(x), f(0) = -1, f(9π/2) = 0

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Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: (cos x+xcost)dt +(sint – t sin x)dx = 0 Ans. t cos x+x sint = c

A:

Q: A power signal which is periodic with period 2n and is characterized by the form f(x) Expand f(x) in…

A: Given, fx=sinhxcosx, -π≤x≤π Since, f is periodic of period 2π then, fx+2π=fx Then,…

Q: (cos y + y cos x) dx - (x siny - sinx) dy = 0

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Q: w= Cos (x+y) + Sin (X-4) Show that dy?

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Q: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

Q: let y=[cos(2x-π)]3 Find y' at x=(π/6)

A: Compute the derivative as follows.

Q: Find f. f(0) = f"(0) = sin(0) + cos(8), cos(8), f(0) = 1, f '(0) = 3

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Q: Find f. f"(8) = sin(0) + cos(8), F(0) = 5, f(0) = 4 F(8) -sin(0) – cos(0) + 5x + 6

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Q: Find The geneval Solution f 3y Cosx + 4x + 2x² e) dx + (3 Sinx + 3) dy

A: Here we have to find the general solution of the given differential equation which is of the form…

Q: Find f. f "(x) = 5 + cos(x), f(0) = –1, f(9/2) = 0 f(x) : %D

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Q: dy Find if y = 4 sin?(3x) dx

A: Here we have to find the derivative of function y which is given as above. Here I am attaching a…

Q: Express y = cos 0 (1 - sin² 0) i in terms of Legendre Polynomials, y = Eo a P₁ (cos 0).

A: The given expression is y=cosθ1-52sin2θ. Our goal is to represent the given expression in terms of…

Q: Suppose sin(u) = -(4/5) 3pi/2 < u < 2pi Cos(v) = -(5/13) pi/2 < v < pi Find cos(u + v)

A: we make two triangles for calculating cosu and sinv

Q: 4. [(3sin 2f – 3 cos 5t )dt 5. sin x dx cos x

A: 4) Given:            ∫3sin2t-3cos5tdt       =∫3sin2t dt-∫3cos5t dt taking constant out…

Q: Find f. f"(8) = sin(e) + cos(e), f(0) = 5, f'(0) = 4 f(e) = 5t – sin (t) – cos(t) + 6

A: Here we have f''θ=sinθ+cosθ, f(0)=5, f'(0) = 4 fθ=?

Q: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

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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.