Find general solution of U" + U = 0.

Q: Show that general solution of the second-order difference equation: ya+2 - Gyk+1 + 8yk = 2+ 3.k –…

A: Solve the second-order difference equation:                      yk+2-6yk+1+8yk=2+3k2-5.3k Find the…

Q: у" - у' - 2sin 2x

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Q: Obtain the general solution valid near the origin: х(х-2)y1+2(х-1)у - 2у %3D0

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Q: y" + y = 2x

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Q: Solve: dy 6- y") +. onn 13-1 Ordineiy Dibgerential equation

A: The solution of the differential equation can be found with the help of the separation of the…

Q: y" - 6y' + qy 2,

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Q: Let 47x + 20 y = 2 is a linear Diophantine equation 1) Show that 47x + 20 y = 2 has integnl…

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Q: Suppose that the characteristic equation of a homogeneous constant coefficient linear equation is…

A: According to the given information, it is required to find the general solution of the…

Q: Obtain the general solution valid near the origin: x(x − 2)y" + 2(x − 1)y' − 2y = 0

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Q: Use the Gauss-Seidel iterative technique to find the 3rd approximate solutions to 2x1 + x2 – 2x3 = 1…

A: we take x1=w, x2=y, x3=z So we need to solve the system  2w+y-2z=12w-3y+z=0w-y+2z=2 Starting with…

Q: П. Solve xау + (3х 2y)ax = U in two ways

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Q: To find the general solution of a second order homogeneous linear equation, we only need to find two…

A: To find the general solution of second order homogeneous linear equation we only need to find two…

Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

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Q: Find the general solution of i = Ax, where A = .

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Q: Verify that y, = e2x and y2 = e5×are solutions of у" - 7у' + 10у %3D 0

A: We have to verify that the functions y1=e2x and y2=e5x are solutions to the given differential…

Q: Obtain 2 linearly independent solutions valid near the origin for x>0 2хy" + 5(1 — 2х)у' — 5у %3D 0.…

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Q: Verify that u = 3x² +3r – 12t – 8 is a solution of heat equation: u, + 2u, = 0.

A: A solution to an equation is the value that satisfy the equation. Suppose that y1 is a solution to a…

Q: 1nd the general and definite solutions of the diIference equations

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Q: A solution of a DE which is not exact and falls under Case 3 i.e. a2 can alone be solved by b2 DE…

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Q: x°y" – 3x'y"+ 6xy'– 6y = 0 -

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Q: 4. Write the solution of i = -y, ý = x, x(0) = 1, y(0) = 0 %3D

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Q: 2 11 3. x*y" – 5xy'+9y= 2x

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Q: y" + y" = 3

A: Solving the given third order differential equation

Q: 4. Solve the IVP: d?s t3, dt2 A. 20s = t5 + 200t – 100 B. 20s = t5 – 200t + 100 s(0) = 5,s'(0) = 10…

A: Given IVPd2sdt2=t3, s0=5, s'0=10sinced2sdt2=t3on integrating

Q: Find the general solution of: az əz 2, дх ду (1+ /z- x – y)

A: The given equation can be written as: 1+z−x−y∂z∂x+∂z∂y=2dx1+z−x−y=dy1=dz2          ......i

Q: х2у" + x(x-1)у' + (1-x)у %3D 0

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Q: 22 To solve y =cy - by' change to u= 1/y?. Substitute for y in um - 2yly³ to find a linear equation…

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Q: у" — у' — х %3D 0

A: We are given: y'''-y'-x=0⇒y'''-y'=x Auxiliary equation is : m3-m=0⇒m(m2-1)=0⇒m=0, 1, -1 Hence,  CF=…

Q: Show that y = - In x + 3x - 5 is a solution of y" -=0. Use y = - Inx+3x – 5 to find y' and y". y' =O

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Q: 1- , L, v² e*dydx 2- S S マーーー ydxdzdy a>0

A: Explanation of the solution is given below...

Q: y" + y = 0, y(0) = 0, y' (5) = 2

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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: If integration using u-substitution technique is used to solve for O u = e4x Ou=1-e¹ O U= u = €²x…

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Q: 2. у" — у' — х %3D 0

A: To solve the given differential equation.

Q: Find the general solution of the given second-order rerential eque 5y" + y = 0 y(x) = %3D

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Q: Obtain the general solution valid near the origin: 2y" + 9ху' — З6у %3D 0

A: Power series solution of the differential equation

Q: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

A: Use the IVT to prove thatx^2+ lnx =1/2 has a solution.

Q: Solve f, e-+ n² dt. 6.

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Q: 2. Solve for y only using Cramer’s rule if: x + y + 2z = 3 2x − 3y +z = 0 3x + 3y +z = 5.

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Q: The equation X2 - 19Y² = 13 has an integral solution, i.e., there is a pair hat x2 19y2= 13. (proof…

A: We have to solve given problems:

Q: Solve the Cauchy-Euler equation: x*y' Зху + 4y = 0. %3D

A: Given Cauchy-Euler differential equation is

Q: 2. x (х — 2)у" + 2(х — 1)у' — 2у %3D 0 |

A: Power series solution of the differential equation

Q: Solve the inizial Nalve pooblem 2xe %3D yco)3=

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Q: y +y² – 1 = 0, Yı = 1

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Q: Then the general solution of this DE is :

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Q: 1 Solve 1 3D7 for z. y. 1-

A: 1x-1y-1z=7

Q: x²y" – 4xy'+6y= 0, y(2)= 0, y'(2)= 4 %3D -

A: Given differential equation is: x2y''-4xy'+6y=0           y(2)=0; y'(2)=4 In Cauchy Euler method we…