The complementary function of (D² +4) y = 3 cos2x is О CF %3D Сј cos(-2x) + C2 sin(—2х) O CF = C1 cos2x + C2 sin2x O None of these O CF = C¡ cos2x – C2 sin2x -

Q: y" + 3y' +2y=(− 4x² − x + 1)cos 2x − (2x² + 2x +1)sin 2x

A: To solve the differential equation of the form y''+ay'+by=A(x)cosbx+B(x)sinbx Assume the particular…

Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

A: To find the value of the given integral ∫sin2xcos2x1+3cos4xdx using substitution

Q: 11. Evaluate f- 2 sin 3x dx 4+cos 3x a.) -2 In 14+cos3x| + C b.) 3 In 14+cos3x| + C c.) - In…

A: Solve by integration

Q: EVALUATE 3 x2 +1 cos dx -1 dx x2 +1 А. cos В. О C. 2/ cos 3 dæ x2 +1 D. 1

A:

Q: (sin 2x)y' = y cos 2x

A: Consider the given Differential equation, sin2xdydx=ycos2x divide both side of the differential…

Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: Consider - 2x 2) (² f(x, y) = e fxx + fyy = 0 cos 2y - e -2y cos 2x. Verify that

A:

Q: Find y' in y=sin¹ (5x5+2x) + Tan-¹ (x²) 1 1 1+x² -(5x5+2x)² A. y' B. y' C. y' D. y' = = 25x¹+2…

A: Given:y=sin-1(5x5+2x)+tan-1(x2)       y'=dydx=dsin-1(5x5+2x)+tan-1(x2)dx…

Q: Sešx cos 8x dx 3x [8 sin 8x - 3 cos 8x] + C A) 73 B) 73 [8 sin 8x + 3 cos 8x] + C C) (8 e3x sin 8x +…

A: MULTIPLE QUESTIONS:   “Since you have asked multiple questions, we will solve the first question for…

Q: cos(t) dt 2/3sqrt(x+5)^5-10(x+5)^(1/2) +C (5 sin(t) + 9)2

A:

Q: dy If y= sec +cos-1(x²), then dx Select one: -2x O a. Vx* -1 V1-x* 2x 2x 2x Ob. Vx*-1 V1-x -4x Oc.…

A:

Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

A:

Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

A:

Q: dy If y = sin(6x – 4), then dx O a. 4 cos(6x – 4) O b. -4 cos(6x – 4) 6 cos(6x – 4) O d. -6сos(6x -…

A: y= sin(6x-4)

Q: 7T 2 Find 35 cos(7x) dx 5π 2 7T 2 35 35 cos(7x) dx = -5π လ

A:

Q: The sin(5x + 2x) dx cos5xcos 2x is equal to 2 In(sec 5x) + 5In(sec2x) +C А. 10 In(sec 5x) +…

A:

Q: y" – 2y' – 8y = 3 cos 2x + 5 sin 2x

A:

Q: Find dy/dt. y cos (rtt-10) %3D Select one: A. -5T COs (Tt - 10) sin(7tt - 10) B.-5Tt sin (rtt - 10)…

A:

Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: F(r) = 5x sin(/2x) – 3 cos(/2x) +xe³r sin(3x) + 2x ?

A:

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y (π/8) = 0…

A: Given,y(x) = C1 sin2x + C2 cos2x + 1 — (1)Here we find the value of C1 and C2 such that the equation…

Q: 2. If y = e-* cos 2x, then f'(x) = %3D

A: Given : fx = e-xcos2x

Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

A:

Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

A:

Q: Find dy if y= 5x² sin4x dr O None -20x? cos4x – 10xsin4x 20x² cos4x + 10xsin4x O 10x² cos4x +…

A: We apply u*v rule of derivatives d/dx (u*v) = v*du/dx + u *dv/dx

Q: 3. f(t) = 2e3t sin 2t 3est cos 2t %3D -

A:

Q: d2y/dx2 +4y=sin3x+cos2x

A: Given that:

Q: when y=cos0 is horizontally factored by a factor of 1/4. y=co s1/4 θ y=cos θ + 1/4 y=1/4 cos θ…

A:

Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

A:

Q: y" – 4y' + 4y Cos 4x -

A: The given differential equation is y''-4y'+4y=cos4x ...................................... (1)

Q: Find and simplify the result whenever possible dx 1. y=x+sin2x 1. y = 4 1 sin' 5x 3 2. y sin5x - 3.…

A: Solving for the number 4:                                          4) y=3xcos(x3)-9 sin(x3)   To…

Q: Solve the he equation F)-5y'x)+8y(x)-4y(x)-xcos(x) 41 19 41 19 sin(x)+ cos(x) -…

A:

Q: Solve the ODE: (7e sin y – - 49y sin(7x))dx + (e“ cos y + 14y cos(7x))dy = 0

A:

Q: 9. Evaluate y' of y = e-2*sin3x a. 3e-cos3x- 2y b. 3e-cos3x- 3y c. 3ecos3x - y d. 3e-cos3x +y e. Not…

A: Explanation of the answer is as follows

Q: Obtain the general solution of 4dx = xVx² – 4dy. Express your answer in terms of cos function

A: The general solution of an ordinary differential equation is the an expression for the dependent…

Q: A particular solution of y" - 3y' – 4y = 2sinx 5 -cosx 17 a. 3 COSX - 17 5 sinx 17 b. 3 -sinx 17 C.…

A: find roots for the homogeneous system

Q: (4D3 + D)y = e2* A. y = c1 + c2 cos 0.5x + c3 sin 0.5x +e2x 33 B. y = c1 + c2 cos 2x + c3 sin 2x…

A: From the given problem: 4D3+Dy=e2x The auxiliary equation is: 4m3+m=0m4m2+1=0m=0  or…

Q: Find the solution of d2y/dx2 +4y=sin3xx+cos2x

A:

Q: 35. Given that d = 6(sin 2x - cos 3x) and y = 0 dx when x = 0, y = A -3 cos 2x - 2 sin 3x – 3 B 3…

A: We can solve this problem using initial value problem.

Q: F.(3e-3 sin(2x')) is equal to 2 3. n 4+@² 3 cos 8 4 3. 7(1+o² 4 cos 4 4 1 3, 1 +4cos 4. 4 2 1+@ 4…

A: Use the following formulas to calculate the Fourier cosine transform. Fee-ax=2πaa2+ω2…

Q: d/dx(sin 3x5) = 15x4 cos 3x5 %3D Select one: O True O False d/dx(1/csc x) = cos x Select one: O True…

A:

Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: Suppose f(x) =sin(3x- 2). Evaluate: A -3cos(3x- 2) +C B ® --cos( 3x – 2) +C © ;cos(3x – 2) + C D D…

A: Topic = Integration Correct option = B

Q: If it was f(x,y)=y cos(6xy) SO a² f Əy² 2² f Əy² a² f Əy² a² f Əy² = 36 x²y cos(6xy) + 12x sin(6xy)…

A: A detailed solution is given below.

Q: Integrate f Osin-15x+C ○ -sin-¹5x + C 1 dx 1-25x2 - 5 H|K sin ¹5x + C cos ¹5x + C

A:

Q: Q2: (a) Evaluate ſ cosx sinx V1 – sin4x dx.

A:

Q: Evaluate the dy/dx> d) y=e-x((cos(2x)) a) -e-x(cos2x+2sin2x) b) e-x(sin2x-cos2x) c)…

A: y=e-xcos(2x)differentiate…

Q: Suppose f (x) =cos( 2– 3x). Evaluate: )dx A - 3sin(3x – 2) +C ® -;sin(3x – 2) + C sin(3x – 2) + C D…

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.