Match the graph to the equation. I T 37 47 5n 67 7n 8n 9n 10n11n 12n -1 -2 -3 -4 -5 O y = 4 cos - 1 4 © -끼) y = 3 sin ( %3D O y= 4 cos 40-1 Oy =-4 sin 40 1

Q: 3. S sin®2y · /cos2y d|

A:

Q: 1. The following system has one root in the first quadrant. Perform one iteration to calculate the…

A: The Multivariate Newton Raphson method uses the formula: xn+1yn+1=xnyn-∂f1∂x∂f1∂y∂f2∂x∂f2∂y-1×fxnyn…

Q: y" - 6y' - 7y = cos2t sin t Find Particular solution %3D |

A:

Q: S √√9-x² dx using trigonometric substitution will lead to: **/2 cos²0d0 Evaluating Ⓒ 18/² A 95*1/2 B…

A:

Q: Graph: y = 2 sin 27x, 0 s xs 2.

A: To graph: y=2sin2πx,     0≤x≤2 Solution: We know, for a sine curve of the form: y=asinbxAmplitude…

Q: The equation C = | 0.40 cos 1.20d0 and S= -0.40 sin1.20d0 are involved in the %3D %3D e study of…

A: Use the following formula: ∫θ1θ2eaθcosbθdθ=1a2+b2eaθ(acosbθ+bsinbθ)θ1θ2   Consider the equation for…

Q: Determine an equation of the graph shown below. 4 21 y = 3 sin 2 x- - 1 Oy- -2 cos 2x y = 3 sin 2 x+…

A: Graph: In a cartesian coordinate system, a graph represents the points of the form x, y, where y is…

Q: Find: O d: x-6,X-1 dy 3 23=Sin (cos 8x)

A: 1 .y=45x3-6x2+x2-12. y=sin(cos(8x))

Q: - 4y = e + 12t sin (2t) 2t Cze 4 + te -3t cos (2t) 4

A: Undetermined coefficient: y''+4y=e2t+12tsin(2t)Auxilliary eq ism2+4=0m=±2icomplementary function is…

Q: Solve the following 1 √√1-3x siny Cos 2y +1 cb₁ x² y² + x³ In x = 1 - 3 xy (a) - dx + dy = 0

A: We have to solve the differential equations given as follows a) 1sin ydx+1-3xcos 2y+1dy=0b)…

Q: Solve for A +능 D %3D B If: A=V8 (Cos ti Sin) %3D 8 = (1+i) c : V2+2i D = 3[2.5 cis los°- 3.3 cis 60]

A:

Q: A B 25/sin² 5 (sec 0 - cos 0) d )* Which of the following is equal to S; x² +25 dx ?

A: The given integral is x2/sqrt(x2+25).

Q: 13 9 2 cos dx dy dz =| 0 0 3y (Туре an exact answer.)

A:

Q: The turning moment T on the crankshaft of an engine is given by T= 6+2.5 sin 20– 3.8 cos 20 Find the…

A: Explained below

Q: Find a particular solution yp for the equation. y" - 6y' + 5y = cos3x 3sin3x

A: Consider a non-homogeneous differential equation of the form a(x)y''+b(x)y'+c(x)y=r(x). Then the…

Q: The equation corresponding to the graph shown below could be:“ (플, 1) (2ñ, }) TT 1 A y = 2 cos x+1 1…

A:

Q: y''''+8y'''+32y''+64y'+39y=e^(-2x)((4-15x)cos3x-(4+15x)sin3x) Find a particular equation for:

A: The given differential equation is: y''''+8y'''+32y''+64y'+39y=e-2x ((4-15x) cos3x-(4+15x) sin3x)…

Q: Match the equation to the graph. y 2 sin 30 - 1 %3D Sn / 3n 7n 21 4.

A: y=2sin3θ-1Use the form  a sin ( b x − c ) + d  to find the variables used to find the amplitude,…

Q: 7L 1 Se cos 2t dt

A: Given,            ∫e7tcos2tdt

Q: 5. Find (b) y = cos (11x + 5x).

A:

Q: What is the equation of the graph below? 0.5 5 T/6 10 0.5 = CoS ( 2x 3 ) y = sin ( 2x + y = sin ( 2x…

A:

Q: 3. The equation that best represents the graph shown below is 4 -2 A. y = 4 sin(2x)+2 В. y =-4…

A:

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…

A:

Q: Which of the following nonhomogeneous equation cannot be solved the method of undetermined…

A: If the term in the non homogeneous part is of the form eax, sinax, cosax, x,x2,..., xn, then the…

Q: V. Find the general solution of the following Bernoulli's Equation. 1. cosysin2xdx + (cos²y –…

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Q: 5. (D² + 16)y = 24 cos 4x – 32 sin 4x

A:

Q: a(t) = -7 cos 2t – 8 sin 2t t Find its velocity and position functions at any time t if it is…

A: Given, The acceleration of a body, at=-7cos2t-8sin2t,  t≥0 At t=0 sec, Velocity,v=4 msec  and…

Q: S cos³y sin³y dy 3.

A: Given,            ∫cos3ysin3ydy

Q: Graph the nephroid of Freeth: r = 1 + 2 sinu/2

A: This graph has period: We try to find x and y coordinates for this graph. theta x y 0 1 0…

Q: A particular solution of the equation y(4) + 2y" + y = 9 cos(t) + 2et – 5t is of the form

A: See the detailed solution below.

Q: 5. Find (b) y = cos (11xs+ 5x).

A:

Q: Sketch the graph of y = 2 cos (r) +1 on the axes below. 4 -1/2 T/2 Зл /2 27 -1 -2 -3 -4 2.

A: Given that: y = 2cos12 x+1

Q: Find the solution to the given equations: (a) y" + y' – 2y = cos(x) – 3 sin(2x), y(0) = 1, y'(0) = 2…

A:

Q: If simple harmonic motion is described by æ(t) = (/2/2) sin 2t + ø, the phase angle is when x(0) =…

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Q: What is the equation of the graph below? (x.0) (22.-2) O y = sin (2x) - 1 %3D O y = cos (2x) - 1 O y…

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Q: i- y' + 2y 4 cos 2x. yT) = 3 (using Bernoulli Equation) %3D %3D

A:

Q: Which of the following equations can be used to describe the graph shown above? oy = 3 sin(2x) + 1…

A: First option is correct

Q: The equation (sin 2.x- 2y cosx) dx = 2dy is linear O yes O No Bernoulli s equation can be…

A: All the questions has been solved with explanation in step 2 and step 3.

Q: -y'-Tany = x" (n # 0) 1 Cos?y

A: We change it into first order linear equation and then solve.

Q: Y Snow that cos30 = 4 cos'0-3 cost, Hence or otherwise. a. Find all solutions of the equation:cos 30…

A:

Q: Find L{(t- 2) (3 cos 5t +1)}.

A:

Q: 2π π14 cosφ SSS p' sinødp døde 0 0 0

A:

Q: 1- y" - 6y' - 7y 2 cos Dt sin Mt Find Particular solution

A: It can be solved by finding C.F. and P.I

Q: Write an equation of the form y = a sin bx or y= a cos bx to describe the graph below. Ty 0 1 nin 1…

A:

Q: 2. xy' - y = y' cos 3x

A: Given the differential equation

Q: (a) y" + 3y' – 2y = -e2" (5 cos 2r + 9 sin 2a)

A:

Q: Question 6 Find the solution. (D4 + 18D2 + 81)y = 0 y = (c, + c,x) cos3x + (c,+cx) sin3x. B y = (c,…

A:

Q: 26. Circle the following equations if they have symmetry about the y-axis. x² + y? = 9 %3D y -3 csc…

A: If we plug -x in place of x and get the same equation , then the function will have symmetry about…

Q: e graphs of 23 57 50 sin (-) 14 25 49 50 y= and y = 50 e ve been plotted on the same axes below. 2 2…

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.