2V5 18. find In y 'dy dy 17. y + 4y In? y 2Vy de dt 19. 20. sec 0 + tan 0 tV3 + r + 2Vx – 1 dx 41³ – 1² + 16t dt 21. 22. 2xVx – 1 T/2 V1 – cos 0 do (sec t + cot t)² dt 23. 24. 6 dy dy 25. 26. Vy (1 + Vezy – - y) 2 dx dx 27. 28. xV1 – 4 In² x (x – 2)Vx² – 4x + 3

Q: Vydy 1+ y\y 3.

A: Soln:

Q: (y² +6y)dy (y+3)² 8.

A:

Q: х dy J(P+4) 12 dt Find for y = dx Choose the correct derivative below. х dy |(? +4)* 12 ( ) 3 O A.…

A:

Q: гуг 0 = fp ( ²4 2² - 62²) + xp (T-H10

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

Q: " + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

A: Given: y''+y=12cos2x-sinx

Q: 3. (D'+ 9) у -D0 %3| Ans. y=c, sin 3x+c, cos3x

A: See below the answer and explanation

Q: y'' + 6y' + 8у = 3e-2х + 2x

A:

Q: i) tanzy dy sin3xdx

A: As we know that  (i)  tan2y=sec2y-1(ii) ∫sec2ydy=tany+C(iii) sin3x=3sinx-sin3x4(iv)…

Q: PART 1: State the characteristics (order, degree, type) of the given DE. 1. (1-x)y" - 4xy' + 5y =…

A:

Q: (3+ 7cos (x)) sin? (x) de 28. 29. sin° (9y) sec² (9y) dy / tan" (2) cos" (2) dz 30. [tan(2t) – sin°…

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

Q: Exexcises E Set 2] Implicit Differentia tion x=x 2. Find dy if dX 1. +Sin xy Find dy if 2x²- 3y'=8…

A:

Q: find dy/dx

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

Q: Find ds/dt when u = 3pai/2 if s = cos u and du/dt = 5.

A: Given,

Q: 7. (y² + 1)dx + (2xy+ 1)dy = 0. sin x dy 8. x dx + 3y x2

A:

Q: 7. fa-4x')"x°dx

A: solution is given below

Q: y = Vr² + VT etin e y = r-5 y = (cos z)n. y = /tan 2x – sec3 (4x – 1)

A: as we are just given 4 functions and not any question so I assume we need to find the derivative of…

Q: 2. (D5 – 2D³ 2D² – 3D − 2) y = 0

A:

Q: e2x dx 4 + e4x 13.

A: We have to find the integral of the given function.

Q: (x’ – 10. 2x +3)dx x-4 c (4v+3)dy

A:

Q: 1. 2y"" — 7y" + 12y' + 8y = 0 2. (D³ – 2D³ – 2D² – 3D − 2) y = 0 - 3. y" + 6y + 8y = 3e-2x + 2x 4.…

A:

Q: 5. (x + y)dy – (x – y)dx = 0. %3D

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 4. Y" + y = 2x sinx

A:

Q: d. Evaluate dx dt (t2 +2t) -1

A: We use the Leibnitz rule of differentiation under integral sign to solve the given problem.

Q: äbäs 25 Q2: Find y(2) if D.E as give (25 mark) Given 2 +3y = sin 2.x, y(0)= 6 dx

A:

Q: , find dy/dx. х • 7x² V2 + cos³t dt 126. y 125. y = V2 + cos³t dt 128. y 127. y = dt 12 + 1 dt 3 + A

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…