Question 1 (Variation of Parameters). Find a particular solution to y" + 25y = 3 sec 5t.

Q: Question#03 Solve by any appropriate method. x*y" + 2r'y"-xy' + xy = x*sin(Inx) Question#04

A: 3. we have given equation  x4y'''+2x3y''-x2y'+xy=x2sin(lnx) ...(i)    now divide equation (i)  by…

Q: Question 4 -e-*) dx Evaluate: A '+C 2 B cosh x +C sinh x +C D – sinh x +C E None (F -cosh x +C 2

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Q: Question 3 What is the general solution of 6y(2y sec2r + tan2r)dx = cos2r(4y- 3sec2x 18y tan2x)dy ?…

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Q: Question 1 : Use Runge – Kutta's method of order four to find an approximate value of y for x = 0.2…

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

Q: x - y | 1 If c = 2, show that z = sin satisfies the equation xzx +yzy = 0. x+y

A: In the question it is asked to prove xzx+yzy=0.

Q: QUESTION NO 2: Differentiate the following (a)Y=6x?-sec-1 5x (b)Y=2cos(x)+6cos-1 OS

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Q: Question 6 2 10 If csc 0 = and cot 0 = 3 find sec 0 3. O sec 0 = 2/10 O sec 0 14/10 6. sec e 21 7V10…

A: Use trigonometric ratio

Q: ст/2 56. " sin(2 mt/T – a) dt -

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Q: Find a general solution to the equation y′ − 3y = e^x sin(2x).

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Q: Question 10 Using the method of Variation of Parameters, the particular solution Y, for the NHLDE…

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Q: 3π/2 3) 14 cos 2x dx п/2

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Q: sec2 t dr 42. dt (п, 4) TT tan t + 1'

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Q: 4-1{ 1 s(s? + 4 ၂။ sin2t.dt

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

Q: Question 3 4. a) Integrate tan (0) sec (0)d0.

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Q: S (1) Find the general solution of the equation IC sin x+ 6. 2 cos x %3D

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Q: Question 4 Solve y at x = pi/3. cotx dy/dx = 1 - 2y, y(pi/4) = 1 0.75

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Q: Question 14 d (tanh -'(cosx)) dx A cschx B) -csCx C) -secx D cothx

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Q: If the equation of motion of a particle is given by s = A Cos ( ω t+? ), the particle is said to…

A: a) The velocity of the particle at time t is ds/dt

Q: Obtain the general solution to the equation. dr +rtan 0=7 sec 0 tan e de

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Q: Sect sec't dt Tari'la)

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Q: Solve the problem. 11) A weight attached to a spring is pulled down 2 inches below the equilibrium…

A: consider the trignometric function is  y= a cos bt the period =2πb=1frequency and    a is amplitude

Q: 2. S cos Vædx

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Q: y = Ceax cos(bx) + C2eax sin(bx); a and b are parameters y = Ce2x cos(3x) + Cze2* sin(3x)

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Q: 20. Given 0 ≤ 0 < 2T, solve tan 0 = - V3. ㅇ ㅇ 警, 뜸 0 1,

A: Given,            tanθ=-3 , 0≤θ&lt;2π

Q: Solve each of the equations. Integrating Factors (y +y cos x – ye*) dx + (3x +3 sin x – 3e*) dy = 0;…

A: Given: y+ycosx-yexdx+3x+3sinx-3exdy =0; y0=-1 ⇒1+cosx-ex3x+3sinx-3exdx=-1ydy

Q: QUESTION 4 The minimum value of n required to approximate dx by composite Trapezoidal rule xe with…

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Q: Question 2) Solve the initial value problem having the initial conditions. (Hint: Each time,…

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Q: Particular Solution of the equation (sin x) y' = y satisfying the initial condition y(7/2)=e is, (а)…

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Q: Question 2 Find the solution to the Bernoulli Equation. (3siny - 5x) dx + 2x²cotydy=0

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Q: Question 02: Solve with suitable condition d'y dx - = 0, where y(0)=2, y'(0) = 3, y" (0) =4, y" (0)…

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Q: 1. (6 points) Find the general solution to the following equation y" (0) + 3y'(8) + 2y(0) = sin 0 –…

A: The given differential equation is…

Q: dx 3xy' + y + x2 y4 = d

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Q: A particular solution of the DE y" + y = tan (t) can be found by the method of undetermined…

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Q: Question 8 Integrate the function. dx V9 - x2 COs:1 X+C 2 cos x+ sin x+C D sin *-C Question 9 413

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Q: * = x- y², y(0)=1, with step size Ax = 0.25 over the interval 0<x< 2. dx

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Q: Question 11 of 20 2 Po Solve (2x-y)dx + (x-1)dy=0 Select the correct response: NONE y+2 In a+ 1+ + C…

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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: Problem 2. Solve the initial value problem. y' = cos x v4 – 3 sin æ; y(n/2) = –1 %3D

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Q: Given the equation sec x tan x dx V sec2 x 1 | If you integrate the given equation, the answer is…

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Q: 3. Given 0 < 0< 2T, what are the extraneous solutions for the equation tan 0 sec 0 = 1?

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Q: How many parameters do we have in the equation y = a cos bx + c sin bx + 4

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Q: Find the solution to the Bernoulli Equation. (3siny-5x) dx + 2x² cotydy=0

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Q: question 6. (D4-5D²-36)y = 0 answer 6. y = k₁ cosh 3x + k₂ sinh 3x + C3 cos 2x + C4 sin 2x…

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Q: i+ cż + x = cos t, e>0.

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Q: A mass weighing 32 pounds stretches a spring 2 feet. If the mass is initially released from a point…

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Q: 1. Solve: sin z cos² y dr + cos? r dy = 0, y(0) : (separation of variables)

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Q: (7/6 sin t dt cost 39.

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Q: Question 12 of 12 fe #0. dz and ye-8 sin 4z = 4z %3D dz dx dz dy II

A: The objective is to find the partial derivatives.

Q: Question 10 [i[cosh:(2x²) – sinh ( 2x³) ]dt is equal to A © Sude xdx E None

A: Integration

Q: Find the solution to the following Bernoulli's equations. 1. y3 sec x dx - y tan x dx = dy

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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.