The particular solution of the following nonhomogeneous differential equation y" – 2y' +y = x² + e¬* by undetermined coefficients is:

Q: 2. x²y' – 2xy = x* + 3; y = 2 when x = 1

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Q: Help

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Q: The particular solution to the nonhomogeneous differential equation y" + 4y' +5y = 10x + 3e-* %3D

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Q: The particular solution of the following nonhomogeneous differential equation y"-2y' +y = x² +e-* by…

A: Given nonhomogeneous differential equation:y"- 2y'+ y= x2 + e(-x)  ;

Q: (4) a general solution of the 4th-order differential equation y +y(3) + y" = 0.

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Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y = a sin x…

A: Eliminating arbitrary constants a & b using derivatives.

Q: x³y"+xy'+4y = cos (2 ln x) bulunuz.

A: See the attachment

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Q: Find the particular solution of differential equation = 4ye* using the given boundary condition: y =…

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Q: What is the particular solution to the dy dx differential equation initial condition y(-3) = 2? with…

A: here is the solution

Q: Determine an appropriate choice for a particular solution for the differential equation y" + 4y = 3…

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Q: Show that y - In(x +1) is the solution of the differential equation of (1+ x*)y= 4x':

A: Use the formula below to perform the differentiation .

Q: The linear Differential equation of any order if there is no constant term s present is known as?

A: We have given The linear Differential equation of any order if there is no constant term s present,…

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A: Here I use The Method of Variation of Parameters to solve the ODE.

Q: 5. The differential equation (3x'e' - 2xx+ (r'e' -sin y ldy = 0 is exact because ON

A: Partial differentiation is needed to be done after identifying M and N

Q: y' - y = 2x? 3

A: Given:   y' - 3xy = 2 x2   To Find: An explicit solution of the above differential equation by…

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Q: Form a differential equation from y = 3cx - 4, here c is the arbitrary constant.

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Q: The independent variable x is missing in the given differential equation. Proceed as in Example 2…

A: Given:y+8yιι =yι2   →1Let yι =u →Ad2ydx2=dydxd2ydx2=dudy=dydxd2ydx2= ududy →Busing Aand B in 1we…

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Q: Find the general solution for the second-order differential equation ¨y + 8 ˙y − 9y = −3 with…

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Q: quation for y (x) with real coefficients if two solutions are cos2x and e3x

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Q: Excrcise 1: 1. Let the following higher order differential equation (1) y/" – 2 y" – 3 y = 3e.…

A: For higher order differential equation,           Let  P0xyn +P1xyn-1+.........+Pnxy =F(x) .....(A)…

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Q: y" + 9y = 9sec²3x %3D

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Q: The particular solution of the following nonhomogeneous differential equation y" – 2y' + y = 4x² +…

A: y''-2y'+y=4x2+ex This has characteristic equation               λ2-2λ+1=0λ-12=0λ=1…

Q: 2. Find the particular solution for the dy differential equation dx = 2xy and y = 3 when x = 0

A: We will find the particular solution of the differential equation , dy/ dx  = 2xy   .

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y ae" + be-ª.

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Determine the general solution of the given differential equation. y(4) + 2ylI + 2yl/ -x = 3e" + 2e™…

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Q: 3. The Bernoulli's form of the differential equation x³ydx+(3x¹-y³dy=0 is

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Q: The solution of the following homogenous differential equation y' = - x+y -is

A: We find the solution of the homogeneous differential equation y'=yx+y

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Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

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Q: ,Find the two values of k for which y(x) = ekx is a solution of the differential equation %3D…

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Q: Obtain the Differential Equation from the given general solution. y = C¡ cos(4x) + Cz sin(4x) + Cx…

A: Use the following formula, to find the solution. ddxcosax=-asinaxddxsinax=acosaxddxuv=udvdx+vdudx

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.