What is the particular solution of (3y2 + 10zy²) dz + (6zy 2+ 10y) dy = 0 when a = 1 and y 2 ? Sry + iey =32 O 3ry + Szy 2y = 25 O 3ly+ Say - 2y = 28 2y 28

Q: Which of the following is a particular solution of the equation y"+y'+7y=4cos2x? O a.…

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Q: 1- If y+3y = 8 then g-solution is %3D a- y+ 6 = 1 In (8-3y) = x +c a.

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Q: Consider the following IVP: 1. y"+a2y = 0; y(0) = 1, y'(0) = 0

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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: Consider the following IVP: y'' -10y' +9y = 5t, y(0) = -1, y'(0) = 2

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Q: 17. Find the general solution of * (4D + 4D3 - 3D² – 2D+ 1)y = 0 y = (Cr+Ca)et +(Ca + C)e y = (Cr +…

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Q: Verify that ry4 +r - 27 = 0 defines an implicit solution of the DE dy 4ry + 2y* + 3r = 0, dr on the…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. The…

Q: Consider the initial value problem: y" +y" - 5y' +3y = e, y(0) = 0, y'(0) = 0,y"(0) = 0 The real…

A: The solution is given as

Q: The general solution of the DE y" + 4y' = 0 where y(0) =1 and y'(0) = 8 is O None of these y = 2 -…

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Q: (b) Show that general solution of the second-order difference equation: yk+2 - Gyk+1 + 8yr = 2+ 3.k²…

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Q: Let y = e2x and y2 = e3x be solutions for a homogeneous DE. Then, %3D is also a solution to the DE.…

A: As per Bartley guidelines we are supposed to answer only one question per post. This post contains…

Q: 4- Find the particular solution for: 3x²y' = 5x – 6xy, x = 2 when y = 1 %3D

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Q: Find a particular solution to 11.5e5t y" – 10y + 25y t2 +1 Yp %3D

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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: 3. Verify that 3e-2x +4e* is a solution of y"- 3y' + 2y = 0.

A: We have to verify that 3e-2x+4ex is a solution of y'''-3y'+2y=0

Q: 1. Find the solution of y" – 4y = 147 et %3D with y(0) = 1 and y' (0) = 9. %3D y =

A: The given equation is y” – 4y = 147 e5t. The given initial conditions are y(0) = 1 and y’(0) = 9.…

Q: The general solution of the DE: ZV=1 is y=x(x+ c) Select one: O True False

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Q: 1. Determine all possible solutions of ²u ex² = d²u oy ² by using variable separable method. 7

A: The given problem is to solve the given partial differential equation by using the method of…

Q: What is the particular solution of (3y + 10zy?) da + (6xy - 2 + 10æ²y) dy = 0 when x = 1 and y O 3x…

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Q: 8. What is the particular solution of 2xyy' =1+y², when x = 2, y = 3 ? а. у%3D5x -1 C. y =V5x + 2 b.…

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Q: What is the general solution of (D° + 14D³ + 49D) y = 0 Oy = (C1 + C3z) cos v7a + (C2 + C4x) cos 7z…

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Q: 1. Find the solution of the IVP; 3y" – 11y' = 2x³ – 5x + 1 + 4y %3| - - y(0) = –1. %3D y'(0) = -2…

A: Given initial value problem is  3y''-11y'-4y=2x3-5x+1 with y0=-1; y'0=-2. Consider the homogeneous…

Q: 6 6 Q1. Verify that y -20t e is a solution of the DE y' + 20y = 24

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Q: The combined family is [1, k, k², 3k] and contains no members that occur in the homogeneous…

A: Only simplify the terms we get the required answer as follows :

Q: what is the general solution of y (1 + 3x ) y - v ? Oy = 4 + 3x + Ce %3D = 4 +3z + Ce" 4 + 3x + Ce…

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Q: 3. Let u(x, t) be the solution to 5ætu, – ut = 0, u(x,0) = 3x², x > 0 - obtained using the method of…

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Q: 7. Find the solution of the IVP: y" + y' – 2y = 4t, y(0) = 1,y'(0) = 2 using method of undetermined…

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Q: Find a particular solution to y′′+36y=60sin(6t) yp=

A: The given differential equation is  To calculate the particular integral let us consider If we put…

Q: 6. Use undetermined coefficients to find a general solution of -2x y" + 5y' + 6y = 3e¬2= +e3z

A: The given differential equation is y''+5y'+6y=3e-2x+e3x

Q: yp = 2 is a particular solution of y" + 2y = 3 Select one: O True O False

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Q: Find the general solution of the DE: y" + y" – 16y' + 20 = 0.

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Q: 1. Show that y = c,x1 + c,x³ is a family of solutions of x?y" - xy' - 3y = 0.

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Q: Determine the particular solution. v" – 2y' + 5y = 0; v(n) = 1,v'(n) = 0 Oy- e(0.04cos(2x) -…

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Q: onsider the following IVP: y'' -3y' -10y = 1, y(0) = -1, y'(0) = 2

A: Given differential equation is y'' - 3y' - 10y = 1 ; y(0) = -1, y'(0) = 2

Q: 19. Show that if y1 is a solution of y′′′+p1(t)y′′+p2(t)y′+p3(t)y=0,y‴+p1ty″+p2ty′+p3ty=0, then…

A: Let y1 be a solution of y′′′+p1(t)y′′+p2(t)y′+p3(t)y=0. Then we have, y1′′′+p1 (t) y1′′+p2(t)…

Q: 2. Is y(x) = 2sin3x + 4cos3x a solution of y" +9y = 0? %3D

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Q: *11. Show that the PDES xp = yq and z(xp+ yq)=2xy are compatible and hence find its solution.

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Q: 10. Find the unique solution of the second-order ivp: y" + 16y = 0, y(0) = 2,y'(0) = -2

A: answer is in next step

Q: 3. Find the general solution of the following DE. y' = 3 (y + 1) O y = ce³x - 1 3y = ce³x - 1 Oy =…

A: Use variable separable to Solve this problem.

Q: The solution of the IVP t(t + 4)y + (t + 4) y =t, y(2) = 2 exists in the interv

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Q: Find the general solution of the DE below. y(5) + 5y(4) – 2y“* – 10y“+ y' + 5y = 0

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Q: 5. The particular solution of y' + y = y¯² when x = 0,y = 2 is

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Q: Find the general solution. 6y(4) + 7y" – 12y" – 3y' + 2y = 0 SHOW WORK.

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Q: Verify that yp = 3e2x is a particular solutions of y" − 6y′ + 5? = −9e2x .

A: Explanation is given below...

Q: 10. Find the particular solution that satisfies the initial condition. xy'+ 2y = 3x² – 5x. Initial…

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Q: 3.41 Show that the Neumann problem v²u = 1 in r+ y<1 au D2 on x+ y 1 does not have a solution.

A: We will Use greens theorem.

Q: 2 The general solution of y +xy+ 9x* - 4 y = 0 is: O a C,J,(3x) + C, Y,(3x) Ob. C,xJ,(3x) +…

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Q: 4x 3z + y + 2z %3D 5x + 5y + 10z = 1 O has 0 solutions O has exactly 1 solution

A: We are asked to find the solution of the system.

Q: The general solution of the DE y" + 4y' = 0 where y(0) =1 and y'(0) = 8 is O None of these OF y = 3…

A: OPTION (b) IS CORRECT. THE GENERAL SOLUTION IS  y= 3-2e-4x