Match the equation with its graph. r(t) = cos(at)i + sin(xt)j + t?k, -1

Q: 3. Solve for y in the equation y = e* sin x + e* cos x - y +c

A: the given equation is y = ex sinx + ex cosx - y +c

Q: Q.5/ A) Find dx for the following equation y = In(x2 + 4) – x tan-() %3D

A: Given equation is y=lnx2+4−xtan−1x2 We have to find dydx. Used Formula:- ddxlnx=1x ddxtan−1x=11+x2…

Q: Homogeneous Find C, if y f(cos 2n) = tan 45° 3(3x + y?)dx-2xydy 0

A:

Q: Solve the following equation for the given conditions y(0) = -1,y'(1) = 2 d²y dy + 4 dx :+ 4y = sin…

A: Given differential equation is d2ydx2+4dydx+4y=sin2x+cos2x      (1) with y(0)=-1, y'(1)=2 Auxiliary…

Q: Find the general solution of tan x dx + y cos? x dy = 0.

A: Use seperation of Variables.

Q: 1. cos?x sin x dy + (y cos³x – 1) dx = 0

A:

Q: dy +xsin 2y = x cos² y. dx Solve the Bernoulli equation.

A: Given: y' + xsin2y = x3cos2y ⇒y' + 2xsinycosy = x3cos2y ⇒y'sec2y + 2xtany = x3 Now, let tany = v ⇒…

Q: A particle travels along the x-axis such that its velocity is given by v(t) = (t25 + 4t) cos (3t).…

A: The velocity of the particle is given by: v(t)=(t2.5+4t)cos(3t)

Q: A heat-seeking particle has the property that at any point (x, y) in the plane it moves in the…

A:

Q: (b) S¤(tan? #)dx (c) S cos(2t)e'dt (d*) S(arccos x)²dx (e*) S (1+ 3x)2 dx Hint: Check for a similar…

A:

Q: dy d'y dx ' dx? 2. If y = sin 2x – 2 cos 3x,the find, at x 0

A: The given function isy=sin2x-2cos3xto finddydx, d2ydx2    at x=0

Q: dy 2х+y 9. Find the general solution: %D dx x-2y а. sec x + tan y b. ху" — у' — 0 с. х? — ху + у? %3…

A: Substituting y=vx

Q: 5. Derive the general solution of x cos? y dx + tan y dy = 0

A:

Q: Please differentiate the functions provided in the two images

A: (i) The given function is

Q: HH F Solve the following equation with undetermined coefficients. What are the coefficients of the…

A: The detailed solution is as follows below:

Q: d'y Find for dr? y = 5x? cos(x) + 13 sin(x) d?y dz? ||

A:

Q: VE-1 x= sec?t b) Find for y = dx sint

A: y=t-1sintDifferentiate w.r.t 't'dydt=sint·12t-1-t-1…

Q: x = e' sint,y = e² cos t at t = 0

A: We need to find radius of curvature.

Q: Find the general solution of the following equations. 4. dy - x² = x dx sin x 5. y-'dy + ye cos x dx…

A:

Q: d²y Answer: 1 . If x = t + cos t, y = sin t, find dx2 dx2 (1-sin t)

A:

Q: Consider (D² +1)y = sin²x_ Using variation of parameters, what is the form of y ,? А y =f cos x + g…

A: As per guideline we have to solve one question Please repost other question again

Q: 5. x = cos 2t, y = sin 2t, 0 <t< T

A:

Q: 14. Solve the equation d?x dx dt +2x sin 3 dr? dx given that at t= 0, x = 0 and %3D dt ment

A:

Q: 4. Find d2y/dx? for the following functions: a) y = sin x2 cos 2x b) y = cos (sec? 3x)

A: Given that  a)y=sinx2cos2x b)y=cos4sec23x find d2ydx2

Q: (a) Solve the equation, = 4e cos 2x subject to the boundary conditions that dxdy d?u du at y = 0, dx…

A:

Q: .2 x cos?y dx + tan y dy = 0

A: The given differential equation is  x cos2y dx+tan y dy=0 Solving the the given differential…

Q: x3 Vx-5 у сos x. sin?x cos3x - Find dy/dx of

A:

Q: Show that the following equation is exact and find its general solution. (3x²y+ 4y + dx + (x + 4x +…

A:

Q: The appropriate change of variables for the dx is Vx²-4 x=2 cosØ O x=2 sec Ø O x=2tan Ø O x=2 sineØ

A:

Q: Which of the following equations is NOT an exact equation? dy=0 B (xy - cos x)dx + (x² – 1)dy=0 (2x…

A:

Q: Given x = sin3t, y = -cos3t, then find at t =. %3D dx а. 1 b. 3 с. О d. 2

A: We need to find dy/dx.

Q: 2T -TT Evaluate: S. (sin x + cos y)dx dy II SII 71I

A: Let give integral is equal to I

Q: The velocity of a particle moving along the x-axis is given by: v(t) = 1 cos(nt), t>0

A: Use the defination of velocity than solve the differential equation by separation of variables.

Q: Find the general solution of the following exact differentia (e + 2ry)dx + (cos y +2a y)dy = 0.

A: As it is given the differential equation is exact si we can directly use the formula of exact…

Q: Find the solution of the this differantial equation. extan(y)dx + [(ex)/(x-1)]dy = 0

A: Hair we use the variable separable method to solve this equation.

Q: 4. Find d?y/dx² for the following functions: a) y = sin x² cos 2x b) y = cos*(sec² 3x) c) y = x²(x³…

A:

Q: Which of the following equations is NOT an exact equation? (2x sin y + y)dx + (x² cos y + x)dy = 0…

A:

Q: Determine the form of a particular solution yp for y"+y cosx

A:

Q: The general solution of the DE dx = cos?y is A y= sec?x В y=tanx + C y=tan-1(x) + c y= cos os-(x) +…

A:

Q: 2. Prove the following equation is exact and hence find its general solution. (y?sinx + xy?cosx)dx +…

A: Given: (y2sinx + xy2cosx)dx + (2xysinx)dy = 0 To prove that the above equation is exact. We also…

Q: Check for exactness and obtain the general solution. 1. (2xy – tany)dx + (x2 – xsec?y)dy = 0

A:

Q: given dy=x+coS X find yuhere y( -1.

A: Using variable separable.

Q: Find the solution of the following: 2. e2x (2cosy dx - sinydy) = 0; y(0) = 0 %3D

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find the solution of the following: 2. e2x(2cosy dx- sinydy) = 0; y(0) = 0 %3D

A: The given differential equation is e2x2cosydx-sinydy=0 It can be re-written as…

Q: (ei-e) dx +x cosh udu = 0 when x = 0; u = 0 1. %3D

A:

Q: evaluate the triple iterated integral.

A:

Q: 4 T/2 a, = f(x)cos(n@,rkdr = "jxcos dx %3D sin 4 cos 2 2

A: Okay I am explaining the marked step.

Q: 4. Solve for in the equations below: dx a) -1 dy y? dx b) cos x – sin y 2 = 2- 3 ) xe+ e = 3"

A:

Q: Find the general solution to the following equations: dy 2+ tan y dx

A: The given is the differential equation which can be solved as shown in step 2.

Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)-pi/6. decimal…

A: differential equation