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: Solve y" - by'tlly - Slt-1), ylo)= 1, y'lo)=0 ylo) = |

A: The given function is  y''-6y'+11y=δ(t-1) The initial conditions are, y(0)=1, y'(0)=0 We find the…

Q: +2 Sar : x

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Q: Let a, b, c be real numbers. If ax' + bx +c = 0 has two real roots a, B where a 1, then show that…

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Q: 2). x2y" - xy + y = x³ V

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Q: Evaluate L{te- cos 4t} g + 2s + 15 b) (s2 + 2s + 17)2 5' + 28 - 15 b) (s + 2s + 17) s - 2s - 15 c)…

A: Note : According to the company guidelines we can solve only first question please post other…

Q: the center-radius of 9x?ー16x+9+9y?t12u=12 the equation Can be obtained by adding both sides of the…

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Q: Solve using MUC. y" +4y=3sin2x 3+3+5+ y = C₁ cos2x+ C₂sin2x - -Xcos2x 4 y=C₁ cos2x + C₂sin2x +…

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Q: 2. Sinx- Cosh

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Q: b) Solve x²y" – 5.xy' +13y = 0

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Q: fray)-Incy)+fan\(2) tahagay alma ea 4lih fx +fy=0

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Q: 3 ation 4x² - yz + 4z³ - 25 = 0 at the point (1,25,-1).

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Q: Solue the guen equaitions %3D

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Q: 1. Find the general solution to the system y' = Ay, where A is equal to: 4 0 1 -3 b) 3 1 81 -1 0 -1

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Q: 4. Find the general solutions of the equations i) ua - 4u, +u, + 2u, = 9 sin(3x- y)+19cos(3x- y) |

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

Q: Solve for x: xy2 + yz2 - 4 = 2x - 1. 3-yz2 b) х %3D у2-2 a) x = *y^tyz2-3 2 с) х %3D 3 — yz2 -у? +2…

A: Consider the given expression.

Q: The general solution of (D²+2D+1)(D²+4)y=0 is A y=(C,+C,x)e+C,cos2x + C ,sin2r B) none of the given…

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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: Find the edlution of the following equstions: (osx<r) a) cosx- casx =0 . b) tan2x = 3 tan X Sin8X .…

A: We have to solve the following equations.

Q: S sin³x /cosxdæ =? O a. ( ?cos'z – cosz) vcosa + C O b. ) +c rt), O d. (cosr + cosz ) /cosz + C C.

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Q: fca)= [- -27パ+, fnd f(-)

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

Q: Solve the IVP y" – 8y' + 25y = 0; y(0) = 2, y'(0) = 2

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Q: Practice Exercises 10 (cos 증 + isin 풍)· (cos 쥬 +isin

A: Given, 10cosπ6+isinπ6·25cosπ12+isinπ12

Q: The general solution of the equation (D*+D)y=-12 is y-+x+ccosx + c,ainx +6x ® y-c, + cx + cycosx +…

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Q: 5) x2. dx = x² + 3xy + y², (c) dr = 2 = 3v, + 3x' (d) (1 - y)' + By - 5x = 0.

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Q: 5. To what expression is 4x°y2 - 108 equivalent to 1) 4(x³y* + 3)(x*y® - 3x²y* - 9) 2) 4(x³y4 -…

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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: solve 19. (a) (3)"- 2~1 2-3 (b) 3° (c) (})² 20. (a) -2-(-2)° (b) –2-3.(-2)ª (e) (금)-'

A: 19) a)530·2-1=1·12=12b)2-330=2-31=123=18c)23-2=322=3222=94

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: -5 .......

A: Given,           12-32ix+yi=cosπ3+isinπ3-5

Q: a) Find an analytic function (or functions) if 2 Ref(Z) = x ² = y ²² + 2 x and fli) = 2i - 1 b) Find…

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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.