(b) u = Vt² + 2vt3 - 1 tan I (d) y = sec I VE-1 (f) y = VI+1

Q: sec" y dy- (f) tan y

A: Topic = Integration

Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

A:

Q: (2y cosx + sin“ x)dx = sin x dy ,when x =",y = 1 5y= 1 %3D X 2

A: 2ycosx+sin4xdx=sinxdy,   x=π2,   y=1:A first order linear ODE has the form of y'x+pxy=qxLet y be the…

Q: (х+ siny)dx+ (хcosy— 2y)dy 3D0

A:

Q: y'sin = y cos a is solvable by?

A: given equation y' sinπx = y cosπx is solvable by separation of variables

Q: 2-) Calcu late +he folloming integ rols by using the integration met hods a)| (hx" +8x²+ 15x) dx dx…

A: We are allow to solve one que at a time

Q: Compute the differential dy for y = -6x° + 8x5. dy =

A: topic - differential equations

Q: 18y sin3 9y2. 10) +3 cos V9y2 + 3 dy + 3 cos

A: See the attachment

Q: tan (VT)+2 dx J Va (sec(VT) – cos(/7))

A:

Q: (2y cos y - x secy-x tan y)dy = (1 + sin y) dx

A:

Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: Compute dy/dx if sin(x) = cos(xy^2

A:

Q: That question please

A:

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

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

Q: solve the IVP x(1-siny)dy=(cosx-cosy-y)dx y(π/2) =0

A:

Q: EXERCISE 1 dy -dx = 0

A:

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: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

A: Solve by differentiation

Q: Find dy/dx 1. sin^−1(xy) = cos^−1(x − y) 2. sec^−1(2y cos x) = x^y

A:

Q: Solve the DE sinx siny dx + cosx cosy dy - O by separation of variables. A sinx cosy - C sin y B cos…

A:

Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: in integrating the function fx cos() dx using intogration by parts, whut would you choose for your…

A: Solution

Q: 2 In sec Vi + tag V + C sec sec z dz %D

A: 35. given integral,∫sec x . dxx = 2∫sec x12 . 12x-12dxlet x12 = u⇒ 12x12-1 dx = du⇒12x-12dx = du

Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

A:

Q: find dy of X sin 2y =YCO52X

A: Given: x sin 2y=y cos 2x To Find: To find dydx.

Q: (cos y- zsee'y) de – sin y dy = 0

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: Use Leibniz's rule to find dy dx dy dx for y= 8x-1 √ (t4-5) dt.

A: Concept: Newton Leibniz Theorem : Newton Leibniz A formula for differentiating a definite integral…

Q: S tan ax secex dx 3

A:

Q: A. = 2x - y + sin2t dt = 4x + 2y + 2cos2t (variation parameter). dt

A:

Q: 4. Evaluate: a) 4 (earctan x)dx o dx b)음 arctan x dx # earctant dt

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: (2y cosx + sin* x)dx sin x dy, when x = y = =,y= 1

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: 5 dy of: y = |x sin 2 + tan (x") dx 4

A: Given function is y=xsin2x+tan4x75 We have to find dydx. Here, we have to use some rule of…

Q: d?x 2 dt2 dx - 5- dt 3x = -9t2 – 1 - %3| - - dx When t = 0, x = 1, = 0, find x when t = 2 %3D - dy

A: The given differential equation is 2d2xdt2-5dxdt-3x=-9t2-1                   (1) to find x(2) with…

Q: 5. dx/dt = (4+x)(y-x), dy/dt = (10-x)(y + x)

A:

Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A:

Q: cos v f(x, у, 2) 3D xz2 af af 2 cos y Cosv siny df = - = - = - dx x2z2' dy dz xz3 XZ af cos v %3D af…

A: Topic:- partial derivatives

Q: dy ху* - сosx sin x . У (0) -2 y(1–x²) dx

A:

Q: V4-z2 z siny dx dz dy 16 3. 16 5 0 16 0 66 0 66

A: The objective is to solve the integral ∫0π∫02∫04-z2z siny dx dz dy

Q: b) Find if e Vt2 +5 dt + siny = x- xcosy rsinx ycscx

A: According to Leibniz' rule:

Q: dy 1. sin 2ycos2y

A:

Q: the initial value DE y' - ytanx = sinx, y(0) = 1 cos 2x 5-cos 2x %3D 4 sin x 5-cos 3x 5-cos 2x В) у…

A:

Q: 1) S 2 sec y (tany – sec y) dy

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

Q: dy sin: 8. x +2y = dx y(2) = 1

A:

Q: d²x + 16x = 1 + 2 sin 4t dt2 dx (0) = 0 x(0) = 0, %3D dt

A:

Q: Find

A:

Q: Find (dy/dx) for: tan-¹(x + y) + In(x³y) = sinh(y)

A: To find dydx for: tan-1x+y+lnx3y=πsinhy