find the general solution of the given equation. 1. y′′ - y′ - 12y = 0 2. y′′ + 3y′ - 4y = 0 3. y′′ - 4y = 0 4. 2y′′ - y′ - 3y = 0 5. 8y′′ - 10y′ - 3y = 0

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

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Q: 1+t? if y' = 3y-y2 for which of the I.C's do we have the guaranteed existence of solution : Select…

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Q: 9. Find the particular solution of y" - 2y' + 5y = 0 y(0) = 1 and y'(0) = -2. An

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

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Q: 1. Find the general solution of the equation y' - y = {y²}{e*}.

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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: 1. If y = r is a solution to (1 – r)y" - 2ry +2y = 0 Find the general solution of (1- r)y" – 2ry/ +…

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Q: ax + y + z 1 We will examine the solutions of the equation according to a. x + ay + % a x +y + az ||…

A: The given system is,ax+y+z=1x+ay+z=ax+y+az=a2

Q: Use the method of undetermined coefficients to find a particular solution to the given higher-order…

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

Q: Give the general solution of y? – 3 y = ху — Зу a) Oln(y - 3) %3Dх* - бх + С b) Oy = C(x – 3)² + 3…

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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: 3x - 2y+ z=35 -4x+y-5z=-36 5x -3y+3z=31   Solve the linear equation using 1. doo little's…

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Q: a) Give a particular solution for y" – 2y' + y = 3e*. b) Give a particular solution for y" – 2y' + y…

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Q: Take y'' − 2xy' + 4y = 0. a) Show that y= ?1−2x^2 is a solution. b) Use reduction of order to find…

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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: (c) 4x?y" + 24xy' + 25y = 0, y(1) = 2, y'(1) = -6 (d) x²y" + 2xy' – 6y = 0,y(1) = 0.5, y'(1) = 1.5

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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: 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)…

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Q: 4. Verify whether the following equation is exact. If possible, solve the equation. a) (2.re +u +…

A: on solving these diffrential equation we will get

Q: Find the general solution (x + 2y - 4) dx - (2x + y - 5) dy = 0 *use Homogeneous, exact or non exact…

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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: 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: Given the equation (2x – 3y) dr + (2y – 32) dy = 0, with initial condition y(-3)= -2. a. Prove that…

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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 +…

A: Let's find.

Q: Use the method of undetermined coefficients to find a particular solution to the given higher-order…

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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: 5. Determine the Particular solution of this equation in terms of Y ( +y = -x'y* y = ) y = G) y = G)…

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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: 5. Find the general solution of (x + y+ 1) dx + (x – 3y – 7) dy = 0 x? - 3y2 + 2xy + 2x x2 + 3y2 +…

A: To find  The general solution of the given differential equation.

Q: Get the general solution of the given differentia equation. 1. (3xy + y?) + (x² + xy)y' = 0 A. x'y +…

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Q: find the solution yl-3y'+2y=e3t , y'(0)=0, y (0) =1 el-2e2t+ e3 t .a 1 3et-2e 3t +-e .bO 2et-3e…

A: We will solve the differential equation using standard methods

Q: 3. Find the constant a so that o(x) = re2 is a solution to y+ay- e =0. 0 4 O 3 0 1

A: ϕ(x)=xe2x is a solution to y'+ay-e2x=0

Q: Solve the initial value problem y''-4y'-5y=0, y(0)=a, y'(0)=8. Then find a so that the solution…

A: Given the initial value problem-                                        y''-4y'-5y=0, y(0)=a,…

Q: Find the general solution of y"-2y'+y=(e^t/1+t^2)+(2t-3)e^

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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: 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: 49. Find the general solution of (2x-3y+2)dx-(3x+2y+1)dy=0 а. х? —Зху-3у? + 2х 2у%3D С b. Зx? — ху-…

A: Please see the answer below.

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: 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: Find the particular solution to the following equation y" + 4y' + 5y = 0 y(0) = 1; y'(0) = -3 Hint:…

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Q: 1) Consider the equation y'+2x y-y'=-2x, x>0. (a) Determine the values of the constants k and r such…

A: On integrating, Note:- order of differential equation is number of constant. In Part(a) solution…

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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Q: 19.) Obtain the general solution for the following equation: 2ydx = 3xdy ;  when x  =2y =-1

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

Q: 1: Find the general solution of the following equations: I. dy_2r+2y-3 X-y-1

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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.