Determine the differential equations satisfied by the following functions. Choose the correct answer by shading the circle corresponding to your choice. 5. y = c1e2t + c2e° -3t cos t o y" – 7y' + y = sin t + cos t о у" +y' — бу %3D 5 sin t - cos t o y" + + y' + y = sin t + cos t o y" + y' – 6y = sin t + 7 cos t

Q: Find the solution of y" + 9y' = 162 sin(9t) + 1296 cos(9t) %3D with y(0) = 5 and y' (0) = 9. %3D y =

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Q: y' = y tan x – y² sec x

A: a. The given problem is                        y'=ytanx-y2secx ; x∈0,π2

Q: Find all solutions of the DE y"– 12 y '+36 y=16 te°* (where t is a real constant)

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Q: 1. If x'y" + xy' + (x². 4 - -y=0 Y=x sinx , and y= y,v. Which of the following x>0 equations…

A: Solution:    Given:                  x2 y"+ xy' +(x2 14) y =0, x.o                 y1 = x-12…

Q: 8. Show that the function y = ex (sin 2x + cos 2x) is a solution of the equation y" — 2y' + 5y = 0.

A: The given function is; y=ex(sin2x+cos2x) And the given equation is; y''-2y'+5y=0.

Q: Find one solution of y" + 2y' - 2y = 3e³* cos(2x).

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Q: 3. Let x² + 4xy + y² = 13. dy • Find dx by using implicit differentiation.

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

Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

A: This question is related to differential equations, We will solve it using given information.

Q: .v" + y = cos x ; when x = 0, y = 0, y' = 1

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Q: h45. Solve for the general solution of y'= sinx + ycotx a. y = (x+ C)sinx b. y = Cxsinx c. y = (x +…

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Q: Find the derivatives ( for the following: (choose Four only) dx 1.y = u3 -3 , x = 1-5u3 2. y =…

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Q: If x'y" + xy'+(x? -y=0 x>0 ,y,=x 2sinx , and y=y,v. Which of the following %3D equations satisfied…

A: Let   y1 and y2be two solutions of the second-order linear differential equation d2ydx2+Pxdydx+Qxy=R…

Q: Find and of the implicit equatio: a 3x?z + y – xyz' = 0 b ye-* + z sin x = 0,

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Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

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Q: If x'y" +xy' + (x2 - -0 x>0 , V1=X 2 sinx and y=y,v. Which of the following equations satisfied by v…

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Q: Show that Y + y = 0_given that y=2 sin x + 3 cos X y"

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: 4. y=x

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Q: Q1:-/ Verify by direct substitution that y, = epx cos qx and y2 = ePx sin qx , are solutions of the…

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Q: Find y'. sin t y = 8 + t %3D y' = %3D Find y'. 2 sin 0 + 9 cos 0 y = %3D sin 0 – cos 0 y' = %3D

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Q: If x³y" + xy' +(x? -y=D0 x>0 ,y,=x sinx , and y3V,v. Which of the following 3 equations satisfied by…

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Q: Find y' and y". y = cos(sin(90)) y' %3D %3D

A: We have to find

Q: ry"+xy'+(x* -y =0 -)y = y = x cosx is a solution of the equation Show that

A: Given               x2y''+xy'+(x2-14)y=0                      (1)

Q: 4. Get the exact a. dy = cos 2x dz differentials of y = (sin 2)² b. dy=sin 2z dz dy = sin 2x d.…

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Q: Find the general solution for (cosx)y' = 1 – y² consider y, (x) = sinx. %3D

A: Given:  cosxy'=1-y2                  1          , y1x=sinx Let y=y1+u be a solution of (1)…

Q: y" + 3y² - 2 = e².sint (Variation of parameters)

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Q: Q1//find the value y and root y" + y' = 0

A: We have to find y and roots

Q: II. Find by implicit differentiation. dx dy 1. 2x? + 2y? =17 2. x'y - xy = a'b 1_1, 3. x y 4. 2x +…

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Q: Find the solution. y'= 1 + 3ytanx 3y cor x=ctanx + 3sinx – sin³x 3y tan?x=c+3sinx – cos?x © 3y…

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Q: i- y' + 2y 4 cos 2x. yT) = 3 (using Bernoulli Equation) %3D %3D

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Q: 21. y = csc 2x 22. y = tan 2 Vx* + 1 x tan x 24. y 23. у x? + 1 1 + sin? x

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Q: I ind the second derivative(y") of the following functions and simplify the final results. 1. y = x…

A: Differentiate using the rules of derivative.

Q: A particular solution of y" - 3y' – 4y = 2sinx 5 -cosx 17 a. 3 COSX - 17 5 sinx 17 b. 3 -sinx 17 C.…

A: find roots for the homogeneous system

Q: 2sim x-1 -y = COST+2

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