The indicated function y(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section 4.2, e-SP(x) dx x²(x) (5) as instructed, to find a second solution y₂(x). 16y" 40y' + 25y = 0; e5x/4 Y₂ = Y₂ = Y/₁ (X) / ² -dx Y₁ =

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A: We have to find the general solution of given DE by given family of function.

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A: Given;  f(x)=2x3 and g(x)=4x+5.

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A: Follow the procedure given below.

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A: topic- composite functions Note: As per bartleby guidelines, we are supposed to answer only first…

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A: topic- limits

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Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =

A: We need to find general solution.

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A: y''+2y'+2y=12+ex

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A: Topic:- application of derivatives

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A: Let's solve for c part.

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A: Given D4-1y=2 sinhx+sinx The auxiliary equation is m4-1=0⇒m22-12=0⇒m2-1(m2+1)=0 Therefore m= ±1, ±i…

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A: We need to find y'(x).

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A: Topic = Functions

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A: The answer as follows:

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Solution ) we have option 3rd  y"+ 4y = 0 Auxilliary equation  m2 + 4 = 0 m2 = -4 m = √( -4 )  m =…

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Q: 3X y 2y = 4y + 8y = 2³x + 8x² 2X <-2X Ans: y = ₁2x + ₂xe + cze -25 X -3X 2 —=== ² + x + x + 1²/2

A: This is a problem related to ODE. Based on the general formula and concept we will answer.

Q: Solve the differential equation by variation of parameters. y" + 2y' + y = e-t In(t) y(t) =

A: The DE is given as , y''+2y'+y=e-tlnt find the solution by variation of parameters.

Q: A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of…

A: A  force 540 Newton stretches 3 meters .a mass of 45 kg  is atteched to the end of the spring and is…

Q: Y₂ = 1/² { Ур 1+cos 2x D²+1 Уp = Ур { Т Ур - D2+1 y, = + { +++ 1 + +7c0$ 2+} D=+1cos +++cos 2x} -4+1…

A: This is aproblem related to differential equation. Based on concept of particular integral we will…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Solve the following ODES by Undetermined Coeff. X X A 1 3X 2 • Y -2y = 4y + 8y = 2³x + 8x² - + 2X -…

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Q: Solve the following ODES by Undetermined Coeff 11 4X y - 16 y = 19,2 € + 60e, y(a) = Y(u). 4X -4X…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =

A: 3y''+2y'+y=0

Q: For y=x²-9x+8, find dy, given x = 1 and Ax = -0.1. dy = (Simplify your answer.) 5 2d

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: elax upx dx

A: ∫1xlnx23dx

Q: Find the general solution of the given higher-order differential equation. y"" - 8y" - 9y' = 0 y(x)…

A: The given differential equation is y'''-8y''-9y'=0 ............ (1)  Equation (1) can be rewritten…

Q: Find the general solution of the given second-order differential equation. 20y" 11y' 3y = 0 y(x) =

A: The given differential equation is: 20y''-11y'-3y=0   So, we can also write as; 20D2-11D-3y=0 The…