Given the initial value problem + ary+2v-0 with initial condition o) -g and to)- A Where g.8are constants. f Yes the Laplace transturm ot yien Ys) sasts tne tng (Hint Recall the formula ds sy+3sY-0. sY" +2sY + Y-0. None of these. s2Y" +3sY +2Y 0. sY" + say + BY=0. sy" =0.

Q: 1.5 1.5 xyn (x+2) dydz (x-2)2 fAxedysa fuse trapezaidal Vule in(x-direction}] fuse simpsae Yule…

A: For the solution follow the next steps.

Q: sec2 (sec-1 æ) dæ ævx? – 1 2 | Detailed solution, 3

A: Given: ∫32sec2(sec-1x)xx2-1dx

Q: Which of the following is a linear equation? O 2ay'dy = (2æ² – y^) dæ I| O sin æ cos? æ dy = (1 – y…

A: We need to find out the linear differential equation, from the given ODEs. This can be done as…

Q: dz at the point (3,2, 1), where z is defined implicitly by the equation z +z²x² – y = 8 Calculate dx…

A:

Q: 1. Decide whether the following stabe ments false . Justify are true or (a) YxeTR, VyeR, x²-y² z…

A: (d) True We have to show that,  ɸ⊆ϕ Let a Set A which is the subset of ϕ, i.e A⊆ϕ therefore it will…

Q: 4- 3- 2- 1- X▶ 1 2 3 ZA 10 4 13 3 P 2 Ty 1

A: we have given 3D cartesian coordinate system

Q: Differentiate. 7 - 6x +2e¯x + +X y=xe Choose the correct answer below. O A. dy dx OB. dy dx OC. dy…

A:

Q: 10e? dz by residue theorem, where C'is the contour z| = 2 1:4 + 52ª Evaluate

A: Complex integration

Q: Determine the direction at t= pie/2 where R is 2sin t i + 2 cos t j + 2t k

A:

Q: Show that the equation dy + 2k possesses solutions of the form Σ 2 c, e cos (a, x+ E,) cos (w,t +…

A:

Q: -. Let fiz) be the branch Z-l+i = exp[(-1+i) log 2], 12/20 ocargz<ZIT and C is the positive oriented…

A: If we parametrize C as: Z=eit,  0&lt;t&lt;2π, then dZ=ieitdt and ∫CZ-1+idZ=∫Cex-1+ilogZdz

Q: Evaluate Sz+1) dz, where C is the straight line path from I to 2.

A:

Q: Which of the following functions do not form a set of fundamental solutions of y" – 4y = 0 Select…

A: We will check every option one by one to find out whether they satisfy our given differential…

Q: Q: Fin dx dfor the following functions: - 1- y = 2cot 2 xcos²(x³+1) V x cos (x+1) 2- y =

A: we have to find the derivative of the following y

Q: 2-89. If F = {3501 - 250j – 450k} N and cable AB is 9 m long, determine the x, y, z coordinates of…

A:

Q: HW If r(H)=6 sin zt ċ+ 6cas ztj + 5tk find T,Ñ, V, a and speed at t-2

A:

Q: du - = In ( – u) +C If u<0, then u A True B False Question 2 8x – 16dx=2 x– 2 dx A True B) False

A:

Q: D. Evaluate et-2 tan vE 2t + 3 S 't² – 2t + 1 e2t

A: To evaluate: ∫et-2e2t, tan tt, 2t+3t2-2t+1dt=∫et-2e2tdt, ∫tan tt dt, ∫ 2t+3t2-2t+1 dt+A,B,C

Q: Given y2 - 2xy = 1 a) Find y' b) Find y" and make sure your answer y" is in terms of x and y only.

A:

Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: 5) Consider the following transfer-function system: Y(s) U(s) 282 + 38 +1 g3 + 582 + 6s +7 The…

A:

Q: dw 21. : 1-cosw A. -tan w + secw + C B. w – cotw + C C.-cotw – cscw + C_ D. -cscw + tanw + C

A: We can find the integral value as below.

Q: 5. Let (ryz)" a) Compute the directional derivate of f(ay2) at the point (1.1,-1) in the direction…

A:

Q: 4. Given differential equation y" + y = csc (t) a. Find the complimentary solution y, that solves…

A:

Q: 2 2メ Q1 find dy for y = Cos ( In x + e

A: we have to derivative with respect to x

Q: step1. Craph ! y= Sin (2x-) Sepa. Ventical translation 2 uniti and vertically, (stretehad or Shrunt)…

A:

Q: dy 2) Find for each function: dx a. y= 5x – 7x² - b. y= Jx 1 y С. x² - 5 d. y Зх +1

A:

Q: thereducedsystem yBY -t -t it CI

A:

Q: If x² + y² = R² (R>0), then K Find K in terms of R. %3D V(1 + (y )² )³

A: Introduction :

Q: 1. Decide whether the folloring stabe ments ae false . Justify true or (a) YxeTR, ¥yeR, x²-y² z xy…

A: 1. a ∀ x ∈  R, ∀ x ∈  R, x2+y2 ≥ 2xy  TRUE. Because,  ∀ x ∈  R, and ∀ x ∈  R we have (x-y)2 ≥ 0.…

Q: Find curlF for F = xyz?i+ x*yz?j+ x*y?zk.

A: Given, F→=xyz2i→+x4yz2j→+x4y2zk→ Used formulas, ∂∂xxn=nxn-1

Q: S. The Converse of the Pythagorean Theorem is used to determine if a triangle is a right triangle.…

A:

Q: 2 sec 0 r drde = x² + y² dydx %3D 0. True False Reset Selection

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.