Use Reduction of Order to find the General Solution: (D2 - 4D + 4) y = ex

Q: Solve (D³ + 3D² + 16D - 20)y=0 when x = 0, y = 1, y = 0, y" = 1

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Q: dx x4 + 4

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Q: Solve the particular solution (D2+3D+5)y = 5e-xsin2x using  D- operator method.

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Q: Find the general solution  (D2 − 2D − 3)y = 0 when x = 0, y = 0, y′ = −4

A: The given equation is,D2-2D-3y=0with the initial condition,x=0, y=0, y'=-4

Q: Find the general solution. 1. (D2 + 3D − 18)y = 0

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Q: Give the general solution of (D5 - 3Dª + 8D² – D – 5)y = 0

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Q: Give the general solution of (D5 + 2D4 + 7D3 – 4D² – 26D + 20)y = 0 -

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Q: Show your complete solution in finding the General Solution of (D³ - D)y = 4x² Use method of…

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Q: Solve the equation using Reduction of Order (D² - 5D + 6) y = 2e* Oy=e+c₁e²x + 2c₂e³x Oy = √² + ₁³x…

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Q: Solve this DE (D2+2D+2)y = e-xcscx

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Q: 3. y" if y = -x² 1 %3D V1-x2

A: Given: y=11-x2

Q: dy = 6x(y – 1)2/3. dr

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Q: Find the solution. y'- y = -xyl/2

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Q: What is the general solution of the equation y '(t) = -4y + 6?

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Q: v2,

A: We use Pythagoras theorem

Q: Give the general solution of (D5 – 3D4 + 8D² – D - 5)y = 0,

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Q: y" – y = 2xe". Y' %3D

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Q: Obtain the general solution. (D^2- 2D + 2)y = 0

A: Using solution of Linear Differential Equations with constant coefficients.

Q: Obtain the general solution.  1. (D4 - 5D2 - 6D - 2) y = 0 2. (D5 - 5D4 + 7D3 + D2 - 8D + 4) y=0

A: According to question, Given differential equation, 1. (D4 - 5D2 - 6D - 2) y = 0 2. (D5 - 5D4 + 7D3…

Q: Obtain the general solution: 1. (D² + 6D + 9)y = 18e 3* -3x

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Q: use Separation of Variables to find the general solution. 2y' + 5y = 4

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Q: Use the method of reduction of order to solve the following equations. 1. (D2 – 1)y = x - 1.

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Q: Show your complete solution in finding the General Solution of (D³ - D)y = 4x² . Use method of…

A: Given that: (D3-D)y=4x2

Q: Give the general solution of (D5 + 2Dª + 7D³ – 4D² – 26D + 20)y = 0

A: Solution:-

Q: y" – 6y' + 9y = :

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Q: Find the particular solution. (D^2 − 2D − 3)y = 0; when x = 0, y = 0, y′ = −4

A: From the given differential equation; D2-2D-3y=0 The auxiliary equation is: m2-2m-3=0 Now solve;…

Q: Find the general solution to(D5 - 2D3 – 2D2 – 3D - 2)y=0

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Q: Find the general solution please. (D3 -D)y =-2(1+x)+4ex -6e-x +96e3x

A: Given that the differential equation is     (D3-D)y = -2(1+x)+4ex-6e-x+96e3x  Here we have to find…

Q: (D²-1)y = x-1, solve using Method of Undetermined Coefficient. %3D

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Q: Q3: Solve the D.E_XỲ+Y=. XY+Y= 7/2/2 y2

A: The given differential equation is  XY'+Y=1/Y2

Q: Find the particular solution: (D4 + 3D³ + 2D²) y = 0 when x=0, y=0, y'=4, y"=-6, and y"=14.

A: Given

Q: Find the general solution by substitution or elimination Q6 A: * = x -2 y +t — х —у+2t dt

A: The system is x'y'=1-21-1xy+t2t Obtain the eigenvalues: A-λI=01-λ-21-1-λ=0-1-λ2+2=0λ=±i The solution…

Q: Solve using method of undetermined coefficients (D²- 2D+2)Y 24 e* sın 3x

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Q: Give the general solution of (D5 + 2D4 + 7D3 – 4D² – 26D + 20)y = 0

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Q: Give the general solution of (D5 – 3D4 + 8D² –D – 5)y = 0

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Q: Find the general solution (D3-3D2-3D+1)y = 0

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Q: Give the general solution of (D5 – 3D* + 8D² – D – 5)y = 0

A: To find the general solution of  D5-3D4+8D2-D-5y=0.

Q: Obtain the general solution. (D^3 - 4D)y = 0 when x = 0, y = 0, y' = 0, y'' = 2

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Q: "D² - D - 2)y= 1 - 2x - 9e -x

A: Given differential equation D2-D-2y=1-2x-9e-x Auxiliary equation m2-m-2=0(m-2)(m+1)=0m=2, -1 hence…

Q: 9. (D2 - 2D +5)²y = 0 %3D

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Q: Is t3 t2 – 2dt , can be solved by 3 methods? -

A: Yes, the above problem can be solved by three different methods. The three methods are as follow:…

Q: Find the general solution y" + 3y + 2y = 3e-t cost + 4e

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

Q: dx =+c 6. 2.

A: We can solve the given problem as follows:

Q: Find the general solution of (D^3- 4D)y = 0 when x = 0, y = 0, y' = 0, y'' = 2

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Q: Solve this DE (D2+4)y = 4cos2x

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Q: (y-7) dy 4 (y+3)3

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Q: Show solution how to find d2y/dx2 , d3y/dx3 , and d4y/dx4  when The given is x = t3 + t and y =…

A: Given: Show solution how to find d2y/dx2 , d3y/dx3 , and d4y/dx4  when The given is x = t3 + t and y…

Q: Solve using method of undetermined coefficients (D²- 2D+2)y 24 e s in 3X %3D

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Q: Find the general solution 4. (D2 – 9)y = 0 - %3D

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