y = e2* (c, cosx+ c, sin x)

Q: 1 2 de 4-cose %3D II

A: Given,          ∫0π214-cosθdθ

Q: determine the annihilator of the givenfunction. F(x) = sin2 x cos2 x cos2 2x.

A:

Q: 3 S² x³ cos x ²dx 6.

A:

Q: Solve for the general solution of (cos x cos y – cot x)dx – (sin x sin y)dy = 0.

A:

Q: Solve the DE: (cos y- cos x)y' +cos y sin 2x=0

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Q: 5. (e* sin y – 2y sin x) + (e* cos y + 2 cos x)y' = 0

A:

Q: (b) (cos(x) (2x + 3))'

A:

Q: Sx' cos(x4) dx = o 1 cos(x*) + c 4 - -1 - cos(x*)+ c 4 1 sin(x*) + c 4 -1 sin(x*) + c 4

A: *concept :- let, x^4 = t then integrate the simplified term cos(t).

Q: + 5x + 6 cos x + 2)dx = e – x + cos a + 2 + c - O 3e* + x³ + 6 cos x + 2x + c 3et + x + 6 sin x + 2x…

A: We need to evaluate the following integral I = ∫3ex+5x4+6cosx+2dx

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

A:

Q: Obtain general solution   y¹ = cos²x cos y

A: Obtain general solution  y¹ = cos²x cos y

Q: SOLVE THE EQUATIONS

A: Given:

Q: 4. If y3 +x³ = sin y + sin x find. dx 3y²-cosy А. cos x-3x2 3y2-cos y В. - cos x-3x2 cos x-3x2 C.…

A: Given: y3+x3=siny+sinx To find: dydx=?

Q: I Eliminate the arbitrary constants -2x 2X Y = C,e cos 2× + Ge sin 3X

A:

Q: Find the general solution of y′−y=sin x + cos 2x using variety of parameters

A: Given that: y'-y=sinx+cos2x To compare the given differential equation with standard form of…

Q: 2. f(x) = x²cos 2 x 3. f(x) = tan x – sec x sin x 4. f(x) = 5. f(x) = 2cos (2 + x³) 6. f(x) = x²ln x…

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Q: sin(4x) cos(2.x) dx n (2x) sin (6x) cos (2x) cos 2. ()= 4 'cos (2x) cos (10x sin (2x) trts 10 (e)…

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Q: y = (sin x +cos x) sec x = sec² x

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Q: 3. Explain graphically: cos x dx = 0.

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Q: Solve if the set of functions (1, x, sin x, e^x, cos x) is linearly independent or dependent…

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Q: ¥2/3 6. cos'x sin x dx 5.

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Q: 8. lim,0 1-cos x 2x2 1 (a) 1 (b) – (c) 0 (d) ; (e) 1. -

A:

Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

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Q: 1. Eliminate the arbitrary constants of the equations below. y ==+c,x – Cos x + c2

A: Given differential equation is y=x26+c1x-cosx+c2. . . . . . . .(1) To eliminate the arbitrary…

Q: 1 Eliminabe the arbitrary constants C,e"cos 2x - 3X SIn 2x + - ZX Y C,e

A:

Q: 6. y = C, cos x + C2 sin x + C3 cos 3x + C4 sin 4x ; C1, C2, C3 and C4 are arbitrary constants

A: The given equation is, y=C1 cos x+C2 sin x+ C3cos 3x+C4sin 4x Differentiate this equation up to the…

Q: 11 Evaluate || sin(y)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) 1 b) (1–cos(x)) e) ,-cos(1) d) 1…

A: This integral can be solved by changing the order of the integral. The order can be changed by…

Q: 7(e)₁² X y= » - [1-171² 2 sec- y = (tan 17 1² ² X y = [cscx]arcsin (cos.x)

A:

Q: (-1)° x*1 (2k –1)! 2k-1 k=0 a) sin x b) cosx c) sin x- x d) cosx-1 e) e* ||

A: Given,

Q: S cos ( x^3 ) dx = * sin ( x^3) + c 3x^2 sin (x^3 ) + c - sin (x^3 ) + c - 3x^2 sin ( x^3) + c none…

A:

Q: sin y = cos x (2 cos y– sin²x)

A: Given siny dydx = cosx (2cosy - sin2x)siny dydx -2 cosy cosx = - cosx sin2x…

Q: 6 Evaluate (a) [ a + (4x-2° dx + (4x-2)* dx (2x-3)2 2x sin (x²+!) cos (x+1) dx

A: AS mentioned by you that "none of these is graded please answer 5. These are practice questions"…

Q: 3x cos 8x dx e3x e3x A) [8 sin 8x - 3 cos 8x] + C B) [8 sin 8x + 3 cos 8x] + C C) (8 e3x sin 8x + 3…

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

Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

A:

Q: 7 sin(x) -dx 2 cos x+5cos(x)– 3 4.

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Q: (2) Show that y=x sinx is a solution to y"+y= 2 cos x.

A: To Show: y=x sinx is a solution to y''+y=2cosx

Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

Q: sin(4x) cos (2x) dx = +(st)(9) (e) None sin sin (con (2x) Cos сов (10х) sin (2x) sin (10x) (e)( (Cо…

A:

Q: 1. f(x) = 2x² – 3x + 4 2. f(x) = e-2x sin 5x 3. f(x) = x cos7 x 4. f(x) = 5 sin 3x – 17e-2x cos 3x…

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Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: 4. Find the absolute maximum and minimum values of the function f(x) = cos²x-3 sinx on the interval…

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Q: I Eliminate the arbitrary constants y = C,e -2x COs 2x + ce <-2% SIn 3X

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Q: Show that y = sin x, y = cos x, and y = a cos x + b sin x (aand b constants) all satisfy the…

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

A: we have to find the general solution

Q: 5. y + 4y= sin x + 3 cos x Ans: y = C₁+C₂ cos 2x + C3 sin 2x + sin x x-co COS X

A: To solve the given differential equation.y'''+4y'=sin x+3 cos x

Q: Evaluate D°(cos x +e-2") A cos x – 32e-2x (B) sin x + 64e -2x (c) - sin x – 32e -2r (D - cos x +64e…

A: Here we have to evaluate      D6(cosx+e-2x)

Q: 4. f(x) = 2 cos(x – 2n)

A: Given:  f(x)=2cos(x-2π)

Q: Evaluate D°(cos x+e-2*) (A - cos x +64e -2x B - sin x – 32e -2 cos x – 32e-2 D sin x +64e -2x

A: Explained below

Q: Solve the equation xdx + sec(x)sin(y)dy = 0 cos(y) = -xsin(x) + cos(x) + C -cos(y) = xsin(x) -…

A: