nd the tallawing differentu equation =d -1Sx +7 +eX cos(3x). the beral

Q: dz az C. Find ax and 4. 5x*y?z-y cos xz = 2x°+y

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Q: ZX = 24, XY = 10, and YZ = 26. Find cos Y. %3D

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Q: Given y= sin3x, dy at a = 3 is approximately

A: The given function is y=sin3x. Differentiate the given function as follows. dydx=ddxsin3x=cos…

Q: dy Given y= cos3x, at r = 1.5 is approximately: da Select one: A. 2.933 В. 2.933

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Q: The value of 6 dz,where C:|z|= counterclockwise, is sinh(z+2) 7-4 O a. O b. 27isinh(3) sinh(3) O d.…

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Q: Q) Lind d/dx of ® xe 1o x+3J = 0 2 2sinx cos y =1 ® x -se cs

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Q: Q4) w(x,y)=x siny +x²- (2x²+3y)² find dw

A: We have to find the total derivative

Q: (d^2 y)/〖dt〗^2 +16y=cos ⁡t

A: The given equation is; (d2 y)/(dt2) +16y=cos ⁡t

Q: 7 Cos X dx e 4 Using the Midpoint Rule, M(50) =| |: %3D

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Q: T T 68. y = sin 3 + 4 %3D -

A: Given data:     The given expression of the function is: y=sin(-πx/3 – π/2)+4.     (a) The general…

Q: Find the solution of ordinary differentral equation X+2xy'-2y=L4xlox -5cos(Inx)

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Q: Eliminate the arbitrary constant/s of this equation to obtain the DE. Express the DE in general…

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Q: dy at t = dx? Let x = 3 cos t, y = 4 sin t. Find 4

A: Derivative Question

Q: dz Find dy x? sin(2y – 5z) =1+y cos(6za)

A: The given equation is: x2sin(2y-5z)=1+ycos(6zx) To find ∂z∂y, differentiate above equation w.r.t. y…

Q: dy Find for y = sin (2x +3) da %3D Ans=

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Q: Given z 13t 9 and y- 169 sin : dy dx d²y da?

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Q: 4. Determine the c, and c2 so that the y(x) = c,e-* + cze8x + sinx that will satisfy the initial…

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Q: . Find the qeueral solution: - 2 dy +5y = ex Cos 2x

A: Complete solution = complementary function + particular integral.

Q: dy Solve the equation sin (r) with initial condition y(0) = –1 using Separation of Variables. %3D da

A: Consider the equation: dydx=sin2xy,    y0=-1 To solve the given equation,…

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

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Q: W = x =t' +7, y=cos(2t), z=4t COS

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Q: FIND Y(s) OF THE GIVEN EQUATION. y" + 4y = cos(t-3)+4t, y" - 6y + 15y = 2 sin(3t), y(3)=0_y' (3)=7 y…

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Q: FIND Y(S) OF THE GIVEN EQUATION. y" + 4y = cos(t-3) +4t, y(3)=0 y' (3)=7

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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: Given y = cos(3x), find O O 3 2- * N O √3 3√3 dy at x = 5

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Q: Q3: B find dy/dx for the following equations : 1- y= e(3-cos4x) cot 3x 2- y =- 2x+sinx

A: Given 1)  y=e3-cos4x2)  y =cot3x2x+sinxwe have to find the derivative

Q: dy cos3x, at x = 1.5 is approximately: dx Given y Select one: А. 2.933 В. —0.235 C. 0.235

A: y = cos3x Differentiating dydx= -3 sin3x

Q: Exercises: A. Find for the following: dx 1.y = (5x+3)6 2. y = sec(2x) + tan(2x) 3. y = In(x²-3x - 1)

A: To find the derivative of given functions.

Q: (b) Find, where y= cos ecx- dx -4x+7

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Q: Q1: Find the length of the cardioid r= 1 + cos 0 0 < 0 <T

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Suppose r(t) = cos(nt) i + sin(at) j + 5tk represents the position of a particle on a helix, where z…

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Q: the Yp Vvnich OllOWing is a particu y" + 2y' + 5y = sin t where A; are constants determined by…

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Q: Find y' at the point (4, 4) where z sin(z² – y²) + 13 = 2² – 3.

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Q: 5) [| dydx 6) y cos xy dxdy 00

A: We need to calculate by iterated double integral

Q: 1 (ysin x + y?) dх — + cosx – 2xy) dy = 0 - \y²+1

A: Consider a differential equation of the form Mx,ydx+Nx,ydy=0. If ∂M∂y=∂N∂x, then the differential…

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

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Q: Find the value of integral | (22 + y² + 2)ds, where C is parmeterized by F(t) = (cos(4t), sin(4t),…

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Q: cos(4x) dx - Find the Cauchy principle value (showing details): J (+5x2+4)

A: Given integral is, I=∫-∞∞cos4xdxx4+5x2+4 So, the function is, fz=cos4xdxx4+5x2+4 Now, consider the…

Q: Find the 2nd solution using variation of parameter. y" + 16y=0; y₁ = cos4x For the toolbar, press…

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Q: dy Given that y =÷-sin3x . Find de 2 18. 4 +3cos 3x A B 4 -3 cos 3x 4 3 cos 3x C +3 cos 3x O A Ов

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Q: (D² – 3D + 2) y = 14 sin 2x – 18 cos 2x

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Q: Find the clerivative of Y. a) y = Sin3x t cos3 x %3D b) y = tan? (x³) c) y=4 sec (5x)

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Q: If Xy +y'=1, find at the point Co,-1) 4P dx 2 5- the value of

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Q: Let y = 78 cos -e. Find dy using any method. Express your answer in dx %3D terms of x only. dy %3D…

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Q: 8 sin r at the point (, 4). e form y mx + b where

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Q: Find a trig substitution r = f(@) that makes 1 dr = cos 0 de. (V4+)3

A: Here we have to substitute x =f(θ)

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

Q: 5. Find Sp√x² + y² dr, where ř(t) = t cos t tsint Ost), 0 ≤t≤ 2π.

A: Given r→(t)=tcosttsint,0≤t≤2π. The objective is to find ∫Px2+y2dr.

Q: S-* cos(x²)dxdy = Q2): Show that 1-y2 %3D 6.

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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.