- 6 3 y =x sin x + x cos 2

Q: Evaluate the definite integral.

A: Given : The definite integral is ∫π 3π 2  cos x ( sin x )sin2 x -14 dx .

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

A:

Q: (D² – 5D + 6)y = 15 sin x – 15 cos x - -

A:

Q: S .2 4. sin x cosx dx

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Q: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

A:

Q: 6. Solve cos.xdx +|1+= sin x dy = 0 y

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Q: 1 COS x dx X - sin x | C. #55. 2)

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Q: y = 2 sin (x+)- 1 TC . %3D 4. 4

A: Function is define everywhere so domain is minus infinity to infinity.  Range of sine function is…

Q: 2e cos 2t

A: Given,       2elncos2t

Q: Evaluate the integrals.

A:

Q: 3 cos (x) sin (x) dx = %3D 2 15 O None 6

A: To find the value of given ∫0π23cos2xsin3xdx

Q: d. cos 3x = 0 %3D e. tan 4x - 1 = 0

A:

Q: r 3n 4 Evaluate sin'x · cos'x dx 5. n /2

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Q: 2 8. y' + ²y = -x²y² cos x

A:

Q: 6 2" – 5 sin(r) + dx 1+x?

A:

Q: 37/2 8 cos x dx T/2

A:

Q: 1/4 (sin x + sin x cos x) dx 0.

A: given

Q: 10) Solve xy' = y+ 3x* cos y(1) = 0, x = 0.

A:

Q: y 1 - y = sin x 0.5 9. T/4 Зп /4 57/4 -0.5 y = cos X -1

A:

Q: 4) y-3y'+2y =e"(1+ cos 2x).

A: First we find out C.F. and then we find out P.I. and then the complete solution is y=C.F.+P.I.

Q: 8) y" - 2y'+ 2y = 2e" cos(x)

A:

Q: 3) y(³) − y(¹) = cos(2x). -

A: Giveny(3)-y(1)=cos(2x)To solve differential equation:

Q: 37. y = sin x + /3 cos x, -2<x< 2m

A: Answer: The curve is shown below:

Q: 2n 3. o (x + cos x) dx

A: Given :

Q: b. f(x) = -3 cos [4 (x -+ 2

A: Givenf(x)=-3cos[4(x-π8)]+2.

Q: 3.x cos 5x dx 5. ( re'/2 dr

A: 3.Integration by parts;∫ uv dx=u∫v dx -∫dudx∫vdx dxI=∫ x cos5x dxu=x, v=cos5xI=x∫cos(5x) dx -∫ (1…

Q: 1) x² sin(y') + xe2 – cos(z?) = 3y– 6z + 8 cos(z?) = 3y – 6z + 8 %3D -

A: Given; x2siny3+xe3z-cosz2=3y-6z+8 Now differentiate partially with respect to x we get,…

Q: 9. e' cos (x) =1+ sin (xy) 10. tan (x – y) = 1+ x2

A: Given the equations 1)ey cos(x)=1+sin(xy)2) tan(x-y)=y1+x2We need to find implicit differentiation…

Q: 5. (D² + 25) y = sin x + cos 2x

A:

Q: B) Evaluate 3n 2 4 y sin(x) dydx 0 0

A:

Q: 3. x = cos³ 0, y = sin 0 4

A:

Q: 22. y' = 1 + 3y tan x. ANS. 3y cos³ x = c + 3 sin x – sin³ x.

A:

Q: 2 3) 9 = x ² sin x y વચ્ચે ઝ 4) y = sin x 1-2 cos x

A:

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: Evaluate the integrals

A: The given integral is ∫-π2π215sin43xcos3xdx.

Q: 5. 2 sin7 0 cos Od0 )dy 1 6. JF(ylny 9-y².

A: Use the method of substitution to solve a given problem.

Q: 5. (D² + 16)y = 24 cos 4x – 32 sin 4x

A:

Q: 8. y"+y = 3 cos 2.xr,

A:

Q: 1o² (sin x + cos x)dx = O 2 O None O 1

A:

Q: 13. (D -1)y = x' sin 3.x

A:

Q: S sin(ax)cos(ax)/3 – cos(2ax) dx

A: Sin(2ax) = 2*Sin(ax)*Cos(ax)

Q: Evaluate the integrals

A: Since, our aim is to evaluate ∫0π2 5(sin x)32 cos x dx.

Q: 2. Eliminate all the arbitrary constants in the equation as follows: y = Ae2x – e-5* (B cos 2x + C…

A:

Q: 7 sin (x)cos(x)dx = + C

A:

Q: 5. (D² + 1)y = cos x. y = c, cos x + c2 sin x + x sin x. ANS.

A: Using method of linear differential equations with constant coefficient.

Q: 2 cos (x) +2cos (x) + 1=0 O A. 4 4. O B. {2x} O C. {t}

A:

Q: 2 y = cos( x 4

A: answer is in next step

Q: (a) y" + 3y' – 2y = -e2" (5 cos 2r + 9 sin 2a)

A:

Q: 1. y" + 4y = 4 cos x + 3 sin x – 8 %3D -

A: Note: -Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 38. y = x cos. cos x

A: