1. Eliminate the arbitrary constants of the equations below. y ==+c,x – Cos x + c2

Q: 2. Eliminate the arbitrary constants of the equation below, where B is a parameter. x = c1eßt + c2…

A: Given, x=c1eβt+c2e-2βtSin 2t-4t3 To eliminate the arbitrary constants of the above equation.

Q: Show that the equation 2²2 2 2²y Əy +2k c². əx² de ² Ət possesses solutions of the form 0 - kt Σ Cre…

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Q: 2. g'-yso ylo)=2 gilo): -2 y'Co)= y'(0)= -2 : -2

A: Given: y''-y=0, y0=2, y'0=-2 So, we can also write as: D2-1y=0   The auxiliary equation is: m2-1=0

Q: Find L[et tsin(2t) - e-2t+3 +e-2t cos 3t]

A: BY USING THE LAPLACE TRANSFORMATION RULES  WE GET OPTION (D) IS CORRECT OPTION.

Q: 1.Suppose that (ax+b)cos x dx=6.Then the values of a equals a) c) 4 -4 b) з d) -3

A: The solution of the problem is given in the next step.

Q: 1. 3. Determine [[e=²*² +25-+²] kt [[e+cos (√2+)] [[ext_H(t-a)]

A: Given : 1. Le-kt+2π-t42. Le-tcos2t3. Le-2tHt-a

Q: 8. If fx) = cos (2x), findf '(). TC %3D a. b. c. 1 d. -1

A: The given function is f(x) = cos2(2x) Differentiate with respect to x using chain rule…

Q: 5. Find the general solutions of the equations i) Zx - 4z,, – 5z, +10z, = cos(x+3y)-sin(x+3y) %3D

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

Q: 2) find the radius and coordinate center for the equation 2x42y+10y-12х-20-0 3) prove that sin 2x…

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Q: Eliminate the arbitrary constants from the following equations. y = e−3x(a cos 5x − b sin 5x) + cx

A: If we have to eliminate arbitrary constant then we have to double differentiate above function with…

Q: I. Solve the given LDE using the method of undetermined coefficients (D^2-2D+5)y=e^x cos(x)

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Q: A. Obtained the general solution. 5.: 6. (D² + 1)y = cos x

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Q: 2 8. y' + ²y = -x²y² cos x

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Q: 14 :Q13 (-9)" (2n)! (a)e (b) cos 3 (d) sin 3 (e) None (c) cos a b C d. e

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Q: The general solution of the nonhomogeneous equation y" + y = x is O y = ce* + Cze* + x + 1 O y = C,…

A: The given differential equation,y''+y=x

Q: 41. Let a, b, r bc constants. Show that k sin rt - r cos rt y = Ce-kt +a + bk k2 + r2 is a general…

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Q: a) z=cos² (3 xy) onde x=p+eº ey=p²-2e³8 b) z=4x³y onde x=3p²+0² e y=p²-40²

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Q: 1. Eliminate the Arbitrary Constant(s) of the following: 1. by xy'-1; b is constant, 2 y=+de; e and…

A: We have to eliminate the constant in the given equation. Here I am solving first two parts…

Q: If y=C,cos2x + C,sin2x+2sinx is the general solution of a certain nonhomogegeous LDE, which of the…

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Q: S 10 -dx may be written as cos10* * Aln|secB"- tanR+ C. where A, B, and C are constants not equal to…

A: We need to choose correct option.

Q: II. Elimination of Arbitrary Constants. In each of the following, eliminate 1. y = C,eax cos bx +…

A: Given:- i.  y = c1 cosbx + c2 sinbx  ii. y = c1x+c2ex To find:- Elimination of arbitrary constants…

Q: 7) Suppose cos(x – y) = xy. Find at the following points 7.1) (0, 5) 7.2) (0,– 5)

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Q: Part C. Determine the Solution of the following DEs Solutions can be not in y-f(x) form. - (y +5)(x…

A: Using variable separable method

Q: 6. y = C, cos x + C2 sin x + C3 cos 3x + C4 sin 4x ; C1, C2, C3 and C4 are arbitrary constants

A: The given equation is, y=C1 cos x+C2 sin x+ C3cos 3x+C4sin 4x Differentiate this equation up to the…

Q: Which of the following is a particular solution Yp to y" + 2y' + 2y = cos /2t

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Q: 1. Eliminate the arbitrary constants of the equation below. y =+c,x – Cos x + c2 C1x - C1x – Cos x +…

A: To eliminate: The arbitrary constants of the equation. Given: The equation y=x36+c1x-cosx+c2.…

Q: /2 6 csc 0 a) [" r° cos 0 dr de 7/4

A: We can evaluate the given integral by using the following formula.

Q: If y=C,cos2x + C ,sin2x + 2sinx is the general solution of a certain nonhomogegeous LDE, which of…

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Q: 30.) Eliminate the arbitrary constant for the following equation:  y sin x - xy2=c 29.) Eliminate…

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Q: II. Which of the following equations does not have a solution in the interval sxs 2 A. csc x =-2 B.…

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Q: 1. Eliminate the arbitrary constants of the equation below. x3 + c1x – Cos x + c2

A: Let's find.

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: 2. Draw the graph z = - cos(y) for 0 < y < 2n, and then use it to help you sketch solutions of y' =…

A: Firstly we draw the graph of z=-cos(y) for the given interval. Then we find the critical points and…

Q: - the solution of the following O.D.E y' = cos(x) +y

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

Q: _13. If y = sin(4x – 5), then what is y'? а. у'3 сos (4x -5) b. у'- 4cos (4x — 5) c. y' = -cos (4x -…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: II: Eliminate the arbitrary constants of the following equations. 1. x- 3x?y = C 2. y = A1 cosx + B…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Suppose that (ax + b) cos x dx = 12. Then the value of a equals: A) 6. B) -6. C) 6n. D) -6T. E) None…

A: Given: - The integral is, ∫0π(ax+b)cosxdx=12 To find: - The value of a.

Q: What is the equation of the graph below? 2 10 15 -1 -2 -3 O y = 3 sin(x) O y = 3 cos(2x) Oy = 3…

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Q: 2 6 5 seco SSS p² sin p dp do de 000

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Q: (1/2 3. x coS TX d Jo

A: Consider the given integral, ∫012xcosπxdx To solve the integral, apply the By-part rule of…

Q: 2 cos(2x) – V3 = 0.

A: Given  2cos2x -√3=0

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…

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Q: 9. Find an appropriate guess for y,. You do not need to find the values of the coefficients. y" +…

A: Given y''+3y'+2y=5e-x+xcosx        D2+3D+2y=5e-x+xcosx The auxiliary equation is,…

Q: 5. Find the general solutions of the equations i) Z - 4z, - 5z, +10z, = cos(x+3y)-sin(x+3y) %3D ii)…

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Q: 2. Solve the IVP y(3) + y" = 5 cos(2.x), y(0) = 3, y'(7) = 1, y"(0) = 0

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Q: This question is designed to be answered without a calculator. Let y = 2 sin (2x) and d'y =ky, where…

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Q: 9. Find an appropriate guess for y,. You do not need to find the values of the coefficients. y" +…

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Q: -2) (2n) (ale tnd (d) sin 2 (b) cos 2 (e) None

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: Find the general solution to y" + 4y/ – 5y = 0. Give your answer as y =?. In your answer, use c1 and…

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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.