y" + y = 5 cos(2x) – 3 sin(x).

Q: 3(sin y- cos y)* dy cos y

A: We need to solve the integral ∫3sin y-cos y2cos ydy Now, we have an identity a-b2=a2+b2-2ab Hence,…

Q: s sin(3x) + cos(5x) – sin sin)ax |dx

A:

Q: Find the particular solution for: y' sin(2y) - cosx = 0, x =when y = 0 %3D 2

A:

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

A:

Q: 3. cos y sin 2x dx + (cos² y – cos² x)dy = 0

A:

Q: Find the particular solution for: y' sin(2y) – cosx = 0, x =when y = 0 %3D

A:

Q: 1. sin'y (2-3 cos y )dy

A: Given: ∫sin3y(2-3cosy)2dy

Q: Find the first derivative of  y = (x – 1) √ (2x – x2)   + arcsin (x – 1), and y = arctan [ (3 sin x)…

A:

Q: ( 2x – sin y) dx – (x cos y) dy = 0 -

A:

Q: dy -is: then dx cos. cos x Q21. If y = tan 1+sin x

A:

Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

A:

Q: .3 Cos x + cos x dx Vsin a 3,

A: Given…

Q: Show that both y = sin x and y = cos x satisfy y" = -y.

A:

Q: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

A:

Q: what is the antiderivative of   (sinx/1+cos2x) dx?

A: Let,

Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: Solve for the first-order DE: y’+y-y^2(cos2x-sin2x)=0

A: Solution: A first-order Bernoulli ODE has the form of y' + p(x)y =q(x)yn Rewrite the form of…

Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

A:

Q: Integral of Sin^2(2t)cos^2(2t)dt

A: Given: ∫sin22tcos22tdt

Q: x sin 2x sin cos x 2 Prove that: dx = 2x- T

A:

Q: y = (sin x +cos x) sec x = sec² x

A:

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

A:

Q: 2. [ * xkbr cos*x- sin 3(sin y- cos y)° dv 10. cos y

A:

Q: fo (9 cos(x) – 2 sec²(x)) dx

A:

Q: x/2 | (cos(x) + sin(2x)) dx of

A:

Q: 3x * y^4 = 5x * sin x + 4y ^ 3 * cos x + 5y * sin x

A: Given equation is: 3xy4=5x sin x+4y3 cos x+5y sin x

Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

Q: Differentiate y = coS 7 + sin4x+ x cos x + 4 with respect to x. 1. 2.

A: the given function is: y=cosπ+sin-1(4x)+xcos(x)+4x3 we have to differentiate the given function with…

Q: COSX sin x dx 4. S 1-ఆశి అరికి న

A:

Q: Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

A:

Q: 2. sin3x dx + 2y cos 3x dy = 0

A: Given equation - sin(3x)dx+2ycos33xdy = 02ycos33xdy =-sin3xdxydy =-sin3x2cos33xdx             Taking…

Q: / sin(In |x|) cos(In |æ|) + dx COS -

A: We have to prove that the given integral is true.

Q: "/2 sin x dx Jn/a V1-2 cos x 4.

A: As per the guidelines  we can answer only one question at a time. If you want to get the answers  of…

Q: 1. § e sin 4x cos 4x dx 2.5 dx Se-2x dx %3D

A: 1) Given:                ∫esin 4x cos 4x dx Apply u-substitution: u=sin 4x⇒du=4 cos 4x dx…

Q: Find the solution of the equation in the interval 0"sx <360 1. cos x+) 3 = - cos x +T3%3D

A:

Q: The position of a particle moving along the x-axis is x(t)  = sin(2t) - cos(3t) for time t>= 0. When…

A: Given the position function, x(t)=sin2t-cos3t

Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

A:

Q: Differentiate y = coS 7 + sin4x+ x cos x + 4 with respect to x. 1.

A: 1) The given equation is y=cosπ+sin-14x+xcosx+4x3 To find: dydx

Q: ( cos nx dx= [cos %3D nx cos nx dx 0. %D

A: We have to find the integral of cos2nx dx from 0 to 2pi.

Q: y = sin(3x) + cos(0.5x)

A: Given: y=sin(3*x)+cos(0.5*x) We have to determine the value of y,where x varies from 0 to 2pi in an…

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

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

A: Solution

Q: sin(2x) dx+cos(3y) dy=0,y(π/2)=π/3

A: Consider the provided differential equation with given initial condition,

Q: 4. cos x dy + y(sin x – 1)dx = 0; when x = T, y = -2

A:

Q: (y2 cos cos x – sin x)dx + (2y sin x + 2)dy = 0 -

A: The given differential equation is first-order non-linear ordinary differential equation:   First we…

Q: 5) sinh(x)cos(y)dx = cosh(x)sin(y)dy

A: A differential equation (Mdx+Ndy=0) is exact if  dM/dy= dN/dx

Q: 3. sin x cos y dx + cos x sin y dy

A:

Q: sin³€ dt to ylomeldon 3.

A:

Q: 2 sinºx cos®x dx

A: here we use integration method, as we seen that the power of the sin and cos are even . so we use…

Q: y = cos 3x a. 3 sin 3x b. - sin 3x c. sin 3x d. -3 sin 3x с.

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.