12y dy 4+9y° sec (t)+3 tan (t)+sin |dt 7

Q: . If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

Q: dt 34. tan t/4 – sin² t dy - Vy dy 35. 36. yV3 + (In y)? x² 1 38. dx 4х + 5 37. :dx /x² + 2x + 5…

A: 34) Solve the integration:

Q: find dy>dt.…

A: Find dy>dt dydt>1 dcostdt=-sint

Q: (a) Calculate S 8(t+ 2)e¬t dt. (b) Calculate 8 (3(t – 2)) (t³ – 1) dt. - - (c) Calculate S 5(t + 4)…

A:

Q: Solve the IVP y" + y' + 1.25y = 0 with y(0) = 3, y/ (0) = 1 O e-t/2(3cos(t) + sin(t)) O e (3cos(t) +…

A:

Q: Given z = 2 cos t + 33 and y = 8 sin²t dz (i) dt dy (ii) dt dy (iii) dr

A:

Q: If y= sin f dt, then dy is dx 2x sin x sin x 2 VX sinx 2x sinx

A:

Q: d3x 2. Verify that sin kt is a solution of the equation in + k3x = 0 %3D dt3

A: Explanation of the answer is as follows

Q: 7. (a) Find dy/dx, when x a(1 + cos 0), y = a (e + sin 0). (b) Differentiate xCOsx w. r. t. (cosx)*.

A: Proceed as shown below...

Q: dy Find the particular solution of 2y- = x+ sin a when y (0) = 1

A: we have to integrate both side , we get

Q: find dy>dt.                                                        y = cos4 (sec2 3t)

A:

Q: find dy/dt. y = sin (cos (2t - 5))

A:

Q: 4. y" + y = tan x. 5. 4y" – 4y' – 8y = 8e-t 6. y" – 2y + y = : + 3e 1+ t2 et 7. 4y" +y = cos I

A: 4. Given, y"+y=tanx

Q: find dy/dt. y = (t-3/4 sin t)4/3

A:

Q: Q3) Find dy/dt of the function y = cos (5sin (t/3))

A:

Q: SO FO %A4 Find dy/dt. y cos(W10t +1 -sin(ot +11 5. sin(~10t + 11) II + 301 +101 sin(~10t + 11) II +…

A:

Q: 3y" (t) – / (t) = e' cos(t) + sin(t), y(0) = 0, y'(0) = 0 -

A:

Q: Find dy/dt, x=4 sin t; y=12 cos t* O 24 cos t O -24 sin t O 12cos t O -12sin t

A:

Q: 11. dw 12. J(Gu - 1)(3u* + 2) du J-scos z + 4 sec" x) dx 13.

A:

Q: d'y dt2 dy + 4 + 3y = 20 sin(t) where y(0): -2, (0): - 4. Find the solution to the IVP %3D

A: firstly we find out CF and then PI and  general solution is  y(t)=CF+PI

Q: SORU 7) S*-[(sint)i + (1+ cos t)i + (sec? t)k] dt =?

A:

Q: Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

A:

Q: Find dy/dt. y= cos ~ 10t + 11)

A:

Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

A:

Q: Solve the DE Ssinx siny dx + cosx cosy dy = 0 by separation of variables. sin y A cos X B sinx cosy…

A:

Q: (b) [(2t – n)0"dt ja- (a) x In x dx (c) 2x sin x dx

A:

Q: A ) Find ſ cos 5t dt dy B) If y = x² +; , x= 2t -5 then find dt

A:

Q: 4. Find dw/dt. 3 (a) w = 5x²y*z4; x = P; y = t z = t5 1 (b) w = 5 cos.ry- sin rz; = X pi y = t := 1?…

A:

Q: Find the particular solution of dy - 2y = x³ sin 4x, y(1) = 2. dx %3D -

A: Using method of Linear Differential Equation.

Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: (1 + cos 2y) dr - 2r dy = 0, y(1) = i %3D Oy = Arctan 2 O y = Arctan O y = Arctan ( 1) D y = Arctan…

A:

Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

A:

Q: Q 3. A. Find 1. £(t2 – 4t + 5)u(t – 3) 2. y-y +2y cos 3x - sin 3x 3. E-- s2 s+1

A:

Q: dz az B. Find əx and ay 3. x eY+ cos xy36xz+5x²

A: partial derivative

Q: dW Find at t=0, if dt .3, W = x*y+ zxy whe x = sin2t, y = cos ?

A:

Q: Find dy/dt. 11) y= cos(N&t + 12) A) -sin(Na 12) B) 2N8t + 12 sin(&t • 12) 4 C) 8t + 12 4. D) -sin…

A:

Q: Q3: Find if: dx 2x dt sinx dt (1) y = (2) y = [ %3D t- 2 X cosx

A:

Q: What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

A: Characteristic equation for the given differential equation:

Q: The distance between two moving objects whose positions are given by ( x₁, y₁ ) and ( x₂, y₂ ) is…

A:

Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…

A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)

Q: d²y 10. dx2 -- 3y = 2e2* +10 sin 3x given that y (0) = 2 and y'(0) 4 dx %3D 29 Ans. 12 e2x +[cos…

A:

Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

A: Solution:

Q: 1 dt xy secx Q1.a) Find if y+J sint+1

A:

Q: Can you help me step by step?

A: Given information:

Q: If x = 3 sin* t and y = 2 cos" t , then find dy at t = dx 4

A:

Q: dy Find dt y = tan ( sin (4t - 3))

A:

Q: By (d) dy 2- = 3t + 2, y(0) = y'(0) = 0. dt By +4 dy + 20y = -3 sin 2t, y(0) = y'(0) = 0. (e) dr² dt…

A:

Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

A:

Q: dy dt 1 Find dx if 2y°t + t°y = 4 and d.x Cos t

A: