Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y(pi/8) = 0 and y''(pi/8) = sqrt 2 .

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

A:

Q: 3. Verify that ysin x-xy =0 is a solution of the equation y(cosx-y)dr+(sin x- 2xy)dy =0.

A:

Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: Use TWO different methods to find the PS of the IVP: sin x + y cOs x = 0 ( y(7/2) = 2020

A:

Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: 1 If z = 2x2 – 3y with u = x² sin y and v = 2y cos x, determine expressions %3D az dz for and du

A:

Q: The approximation of I = = co cos (x²+5) dx using simple Simpson's rule is:

A:

Q: Consider the following IVP: y +y = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

A:

Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

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

A:

Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: 4. Evalaute cos(x) sin(x) dx

A: Given:

Q: Suppose that 2x² - y² = t² and x = t cos 0. Find (a). ¹(2), X and 0

A: answer is in next step

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

A:

Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

A: Given: fx,y=3x3siny-y2cosx-2ylnx-xlny-4xy2

Q: Show that : y' = 1 when y(x) = sin-(x) %3D V1– x2

A: Differentiation is done in many ways. Some of the rules of differentiation are illustrated below :…

Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

A:

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. y(x) =…

A:

Q: π/2 1-z [²6² x cos ydzdydx = = [Show your solution.]

A:

Q: Find the general solution to 2- ди u = xt + x cos t + t sin x. 3 - -

A: Given: 2∂u∂t-3∂u∂x-u=xt+x cos t+t sin x

Q: 1- Find the equation of the tangent to the curve y = 2 sinx+ cos2x at the point x n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

A:

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

A:

Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

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: 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: Find the value of parameters € and ¶ that makes f(x)=€x+¶ if x<0 and f(x) =2(¶+€)sin(x) +…

A:

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

A:

Q: Find an approximate solution, accurate to 5 decimal places, to the equation cosx=x2 that lies in the…

A:

Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

Q: Use the method of undetermined co – efficient to solve: y'' + 2y = sin (x)

A:

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: (9) Verify that Yp = sin 2x is a solution of y"– y = -5 sin 2r and use it to find the general…

A:

Q: 2 Given that: J2(x)=-, cos.x + sinx find J(x)

A:

Q: The 32nd derivative of y = cos² 2r is O 26* cos 4x O -24 cos 2x O 24 sin 4x O 22 cos 2x

A:

Q: 1. Find for the following functions : dx 4i) y-bmcx* +2y}kos x (ans.: 4x.cos x - 2 In( x² + 2 )sin x…

A: To find the dy/dx of  y=[ln(x²+2)²]cosx

Q: B\ Suppose that = 4 cos² t , x = d²y =- V3 sin(2t) and 0 <t <n. Show that sec3 (2t). dy 2 tan(2t)…

A: Dear student, there is a mistake in the question. The second derivative should be…

Q: Find at the point (1,0) for cos xy + ye* = 0. dx

A:

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

A:

Q: 2 2 sin (2t) dt. 8 - cos (2t)

A:

Q: Find at the point (5, -1,5) where z is defined implicitly by the equation y°z + x cos z = z sin x.

A: Differentiate both sides partially with respect to y

Q: (9) Verify that yp = sin 2x is a solution of y" – y = -5 sin 2x and use it to find the general…

A:

Q: Find [(1 - cos² t)dt]. dx A. sin²x B. -sin²x C. 1 - sin²x D. - cos²x

A:

Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: v² operates on sin(-3x) + cos(3y)

A:

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

A:

Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

Q: Determine the general solution of (cos(x)cos(y)-cot(x))dx=(sin(x)sin(y))dy

A: Given: cos(x)cos(y)-cot(x)dx=sin(x)sin(y)dy