find the general solution of the given equation. 1. y′′ + 9y = 0 2. y′′ + 25y = 0 3. y′′ - 2y′ + 5y = 0 4. y′′ + 2y′ + 4y = 0 5. y′′ + 4y′ + 9y = 0

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A:

Q: Find the general solution of y' + (1/3)y = exy4 Show your solutions on a separate sheet of paper. A)…

A: Solution

Q: 3. Find the values of m such that y =e is a solution of the following equations a) 3y"-5y'= 0,

A: The given differential equation is                                                        3y''-5y'=0…

Q: 1. Solve y' = "ty´, with initial condition y(1) = -2. x2+ +y? xy

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Q: y"-5y'+6y=e'; y(0) = 1, y' (0) = 1

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Q: 4. For the DE y"-3y' x+3e", write the solution of the homogenous equation y., then write a…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: find the particular solution to y’’ + 5y’ − 6y  =  6t + 7

A: y"+5y'-6y=6t+7Auxillary eq f(D)=D2-5D-6Q = 6t+7Particular Integral be denoted by…

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A: here we only need to find particular solution which is easily done by initial guess of particular…

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A:

Q: Find the general solution or unique solution for the following equations. For the fullcredit, your…

A: There are more questions in the image you have attached. But you have marked a blue line to the…

Q: the general solution to  y′′+6y′+25y=0

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Q: If y=e' is a solution of the DE: ty"-2(t+ 1)y'+(t +2)y=0 Then the general solution of this DE is :…

A: The given differential equation is: t…

Q: 4. Find the particular solution of xy' – 2y = -x; when x = 1, y = 5 C. y = x - 2x² d. y = 2x – 3x…

A: Given that: xy'-2y=-x; when x=1, y=5       NOTE: As per our answering guidelines, we can only answer…

Q: 19. Find the particular solution of y" + 4y' + 5y = 2e* a. y =e* b.y =e* c. y = -e* d. y =e* 5

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Q: A second order Caushy – Euler equation having a solution y(x) = x-2cos(4Inx) is x?y" + 5xy' = 0 O…

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Q: Find the general solution to the equation ty" – 3ty' + 4y = 1 - (for t > 0).

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Q: The solution(s) to the equation 3t2 - 2t -1 = 0 is (are):   a. t = 0   b. t = 1/3   c. t =…

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Q: Solve for the particular solution of the following non-homogeneous DE. y” - 4y - 12y = e6t

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Q: Which of the following is the solution of ди +2- ди Ox 0 = a) u(x,y)= e"-2x b) u(x, y)= (2x + y)³ c)…

A:

Q: 3. Find the values of m such that y=e is a solution of the following equations a) 3y"-5y'=0,

A:

Q: Given the initial condition y(1) = 4, what is the particular solution of the equation y' = y (2x +…

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Q: Find the general solution: (a + 2y - 1)da - (2x +y-5)dy =0 A (a-y-2) = C(z+y-4) OB. (2 y-2)2 C(r-y+…

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Q: 19. Find the particular solution of y" + 4y' + 5y = 2e* a. y ==e* b. y = c. y = -e* d. y = e* 5 O A…

A: To find out the particular solution.

Q: 25y" + 10y' + y = 0 Which of the following is a solution of the equation none of the given equations…

A: We have to solve given problem:

Q: Find a general solution to the following higher-order equations. (a) y"' - 5y" + 5y' + 11y = 0 (b)…

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Q: Consider the IVP: y" + 9y = 40ex ; y(0) = 5, y'(0) = -2. Find the general solution.

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Q: Solve the DE: (2-x) y³ +(2x-3) y'' - xy' + y = 0, x<2, given that y(x) = ex is a solution of the…

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Q: The form of the particular solution yp for the DE (D^2 + D - 2)y = 2x - 40cos2x should be yp = Q +…

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Q: the general solution to xy''+y'=0

A: Given query is to find the the solution of differential equation.

Q: / How.I Find the general Solution of : (0x - Ox Dy - 6:D*y )U = 0

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Q: 5. Find the general solution of (6x - 7y) dx - 14xy dy = 0 A. x(2x? + 7y²) = C B. y(2x? + 7y2) = C…

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Q: Find a particular solution to y′′+5y′+4y=15te^2t

A: We find a particular solution to y′′+5y′+4y=15te2t.

Q: %3D A particular solution to this equationy" + 3y+y3xe* can be obtained: Select one: a. by both, the…

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Q: Obtain the particular solution of (3x? - 2y-)y' = 2xy; x =0, y=-1. A x² = 2y²ty+1) B x² = y²ty+1) c…

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Q: 5. Find the general solution of yy' + y² = x a.y = x -+Ce-2* b.y² = x ++ Co-* c.y² = x -+ Ce-2r…

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Q: Find a particular solution of y''− y' − 6y= e^2x

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Q: general solution to (x2 + 1) y′′ - 4xy ′ + 6y = 0 (x2 + 1) y″ −4xy′ + 6y = 0 is given by Select one:

A: (x2+1) y" -4xy' +6y=0Let y = ∑h =1∞n an xn be the solution theny' =∑h =1∞ n an xn-1  , y" =∑n=2∞ n…

Q: 6. Determine the General Solution of this Equation in terms of C y2-x+e2x =DC y+x-e2x C. None of the…

A: To find the general solution of the differential equation in terms of C :            dydx+1xy=xy2

Q: 1. Find the general solution of the following DE: c) y"-9y = 0 d) y"-6у'+ 9у 3D0 a) y"+3y'+ 2y = 0…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other part…

Q: 17. Find the general solution of (D² + 3D + 2)y = e* + 3 3 a. y = ce-2* + cze¯* + xe¯* + c.y = ce-2*…

A: Option A

Q: 1. Determine the values of the variables to satisfy the equation using Jacobi. 5a - 2b = 40 Ans. a =…

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Q: 2x2yn+3xy'-y=0 , x>0  in the equation given as: y1(x)=x1/2 ve y2(x)=x-1 verify that there are…

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Q: Find the general solution of the following equation valid near the origin: (1+4x2)y"-8y=0 00…

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Q: For what value of k the linear Diophantine equation 21x + 14y k has solution k = 1 b) k = 36 e) k=…

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Q: Obtain the particular solution of (3x² – 2y²)y' = 2xy when x = 0,y = 1. a. x2 = 2y² (y + 1) c. x2 =…

A: Let's find.

Q: The solution of the equation у" +8y'+16у 30 which satisfies y(0) = 4 and y'(0) = 2 is O a) 4 e-4t _…

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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.