The solution of the initial value problem y" – 2y' + y = 10 sin(t), y (0) = 1, y (0) = 0 | %3D y = cos(t) – 4et + et . 4t y = 5 cos(t) – 4e – et . 4t | y = 5 cos(t) + 4e* + et . 4t y = 4 cos(t) + 2 sin(t) – 3et cos(t) + et cos(t) y = 5 cos(t) – 4e² + et . 4t |

Q: A particular solution of y"-y'-6y=2sin(3x) cos(3x)-5sin(3x) -cos(3x)-3sin(3x) a. b. 8 13 C.…

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Q: What is the general solution of (1 + a2) y' = x*y %3D Oy"-3ay + 1 = C O ay - 3ry + 3y% tan-1 æ + 1 =…

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Q: y" – 2y' + 2y = e2= (cos r – 3 sin r) (undetermined coefficients) %3D

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Q: FIRd the general solution to y'" +(1) y"-12 y-0. None y c, e+c, sin(2-)+c 6 Cy Cos(2 0) y-c, oc…

A: Consider differential equation: a0yn+a1yn-1+.......+an-1y'+any=0 Write auxiliary equation…

Q: 5. (e* sin y – 2y sin x) + (e* cos y + 2 cos x)y' = 0

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Q: 3. y'=1+cosx−ycotx;y()= -ycot.x:y()= {y= /3 2 sin r 1 cot x+=sin x}

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Q: cos(2) is equal 1 اخترأحد الخيارات 2-2 sin(z) dy dx dz 2 – z 4-2 r/2 sin(2z) dy dx dz 4 - z z-2 cx/2…

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Q: The solution of 1y"+ y' = 0, y (0) = 0, /(0) =1 /(0) = 1 %3D is y(a) = %3D (A) cos a (B) sin a (C)…

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Q: If y = cos x + sin 2x, find the value of y" - y + 3) O 2 cos x + sin x – 2 cos 2x – sin 2x O 2 cos x…

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Q: Integrate | 2 sin O de а. 3(cose)d

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Q: Solve b part only now in 10 min

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Q: y" + 4y + 5y = 50t, y(0) = 5, y'(0) D a.e-2t (13 cost + 11 sin t) + 10t² - 8 b.e-2t (13 sint + 11…

A: The given IVP

Q: Solvecos (2) O a. O b. 2 с. d. y cos Y I - [2 in (2) + co. (:)]* - = 0 dz y sin () = c C = сх ysin…

A: Given differential equation is yxcosyx-xysinyx+cosyxdydx=0       (1) Simplifying (1), we get…

Q: The equation ? + sin(xy) + C = 0 is the general solution of O y' + cos (xy) = 2 (x + y) 2 (ydx +…

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Q: where O O O y(t) = (f-cost)-(1)[(1 − 6) - cos(t = 6)] + 6 sint +4 cost - sint) ([(-6)-sin(t-6)] + 6…

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Q: The special : to the equ gA (D'+1)y(x) = tan(x) %3D

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) -…

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Q: The solution of у" + у 3D 0, у(0) — 0, у'(0) — 1 is y(a) = (A) cos x (B) sin x (С) 1 — е ӕ (D) 1– eª…

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Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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Q: 2) y"+y' - 1 = 3 cos(x)

A: 2.

Q: y = 2 sin(2x) +11 30 30 30 Park 8. y = cos(36) 3- 1 537x 2 424 4 sin)-1 9. y 45 . 2 34 36

A: Note: Since Multiple Questions are asked, I am solving the first question, Kindly ask other…

Q: The general solution of 4y"+4y' +y = 0 is ()%3D

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Q: Solve 2 E| #(0) = – 2, y(0) = 10 y' 29 - 9

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Q: 2- y" + 4y' + 20 y = 23 sin t - 15 cos t y(0) = 0 , y'(0) = -1 %3D

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Q: -(v/y)- o None of the above () ferentia uation y"+y' = 1? What is the general solution of the dif-…

A: given differential equation :-             y''' + y' = 1

Q: - (D' - 4)y = x'e"

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Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

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Q: Find the particular solution : y" + y' + 4y = cos3x 3 5 3 5 (a) cos3x -; sin3x (b) Yp = cos3x -…

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Q: ution of yl = x+xy2 W

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Q: Solve the initial value problem y"-4y'+8Y3D0 for y(0)=1 and y'(0)=2 O A. y = e“ cos(2t) 2t %3D O B.…

A: solve :

Q: if  x²v+sin(xu)-yv²+u³v=1 x²u-2yv=1 ، cos(xu)+yv=5  ,find dy/dx

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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.