In what form should the particular solu tion be sought for the equation y(4) + 2y"' + y'" + 2y' = xe-2x ? A) yp = Axe-2*cosx B) y, = e-2*(Ax + B) с) у, 3D е-2*(Ах? + Bx) D) yp = Ae¯2x E) yp = (Ax + B)cosx + (Cx + D)sinx

Q: (D³ - 5D² + 17D-13)y=0; y(0) = -1, y'(0) = -4;y" (0) = 17

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Q: x'*x13 x*y° *x°y* b13c *b 1°c3 X' 9x * 8x° -3y * 6y? 3x'y®z° *8xy°z®

A: We have to simplify the following... 1. x7*x132. x3y9*x2y-43. b13c*b-10c34. 9x3*8x95. -3y8*6y-26.…

Q: Solve the following exact equations, implicit general solutions will suffice: a) (2xy+x^2)dx +…

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Q: If you are to integrate a certain equation by Trigonometric Substitution, what must you substitute…

A: We are given an equation: -162 + y2  We need to find the trigonometric substitute  for "y" for…

Q: Find the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Please solve number 3

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Q: #2. Define the operators 33/32 = 1/2 (3x +²y), 32= 2 (x-7) = u(x, y) +iv(x, y), show that (af (3) =…

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Q: Example 4: Solve iv) y" + y = sin2x.

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Q: Solue the guen equaitions %3D

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Q: Find the solution. (D³ + 6D² + 11D + 6)y = 0 - 3x B y = c,xe"+c,e – 3x -3x Dy=c,e-+cze+cze*

A: 21 Given differential equation is D3+6D2+11D+6y=0. We have to find the general solution of the given…

Q: answer each question by true or false and explain 1) L{t * e³t} = L{te³t} 2) L-¹{L{t* et}} = t * e³t

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Q: a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit…

A: In this question, we will find the solution to the given problem.

Q: What are the 4 roots of z in the equation: z^4=1

A: Given equation is z4=1 To find : roots of the given equation

Q: y" = 5sin (2z) denkleminin çözümü aşağıdakilerden hangisidir? %3D

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Q: 1) What are the imaginary roots for the function p(x)= x^4 −8x^2−8x+15? You will likely have to…

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Q: • Solve the equation using homogenous equation (5v-u)du + (3v - 7u)dv = 0 a.)(3v +u)² = c(v - u)…

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Q: 7.) Solve а) y'+y'-by=0 6-) у"-ну' +13y=0 с.) у" -бу' +ац=0

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Q: Find all complex z that solve the equation z^12 = −1. Which of these solutions also solve z^4 = −1?

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Q: 1. (r - x) + (-2r + 3x) 2. (-y + 3) - (v - 2) 3. (-3a* + 4 + 2a') -(2 + Sa - a) 4. -(6 - b + 4b')…

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Q: y"+y' + (a) -5 x-b = 0, Xo = 2 is 5. (b)-3 (c)-2 d)-8 Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c)…

A: We have given the answer in the next step. Hope you understand that

Q: 4) Find the adjoint of the operator Lu = u" + 4u'- 3u, where u'(0) = -4u(0), u(1) = -4u(1).

A: The objective is to find the adjoint of the operator, Lu=u''+4u'-3u where u'(0)=-4u(0), u'(1)=-4u(1)…

Q: -24 y"' + 4y" + 9y'+ 10y = when x = y = 0, y' = -4, y" = 10

A: y′′′ +4y′′ +9y′ +10y=−24e−x  Linear non−homogeneous differential equation with constant…

Q: #1. ca) perform the operation (1-√32)-10 (6) Find the cubic roots of 1+√3 2. Express your answer in…

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Q: 1) S“(cosx)" dx. 2) Г(-4). 3) В (10,9) 4) Sº x° e-2* dx Ja-x)i 5) o

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Q: Look for the annihilator of the given expressions. i) e2x sin3x ii) x³ e4x iii) 5x* - 2.x + 8x - 7…

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Q: In what form should the particular solu tion be sought for the equation y(1) + 2y" + y" + 2y' =…

A: Consider the equation y4+2y'''+y''+2y'=xe-2xThe characteristics equation of the homogenous equation…

Q: Calculate the imaginary part of  ∮C(Re(z)+3.78)(2z^2+ 5z+ 13 / z)dz  where C:|z|=1  Use FOUR…

A: We have to find the imaginary part of the integral ∮ fzdz, where fz=Rez+3.782z2+5z+13z over the…

Q: 2) у" + 4у %3D 8x?

A: Given:

Q: 1. 4y" — у 3 10 2. (D3 + 2D?)у %3D— 4 3. уМ) — 4y" %3D х — 2

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Q: -3 8x°y² ' 12x'y* 6.,2 4 17m m m+5 5х-2 13 - x(x-7)

A: To find the LCD

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.