Solve the differential equation dy = x²e¥ dr by the separation method, and determine it the solution that intersects the x-axis at x = 1.

Q: Find the Differential equation by eliminating the arbitrary constant  x2-y2=a2

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Q: 20. x" +4x = 3e2"

A: We have to solve the differential equation using the method of undeterminedcoefficients and no…

Q: Solve the differential equation by variation of parameters. 1 y² + 3y + 2y = 2 + ex

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Q: $2. x" – 4x' +3x =te".

A: Given that x''-4x'+3x=tet To find the general solution :

Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) -…

A: It is given that the differential equation is 2y''+y'-y=x+5 The auxiliary equation is 2r2+r-1=0…

Q: Find the differential equation whose solution is given by: y^2=4ax

A: To find the differential equation for y2=4ax differentiating this equation with respect to x.

Q: Solve the differential equation with appropriate method. Express final answer free of fractions and…

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Q: differential

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Q: Find the general solution of the differential equation.

A: given,

Q: Solve the differential equation by variation of parameters. 4x e2x y(x) = y" - 4y =

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Q: Solve the differential equation by variation of parameters. 4x e2x y(x) = = y" - 4y =

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Q: solve the for the general solution of the differential equation( linear homologous equation): (D2 +…

A: We have to solve the differential equation: D2+2D-1y=0 The given equation is in symbolic form where,…

Q: Solve the differential equation. xy' + y = 4Vx

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Q: Solve the differential equation by variation of parameters. 4y" - y = ex/2 + 8 y(x) =

A: First I have find the complementary function and then by using method of variation of parameters…

Q: (b) x" – 2x' + x = 4e'.

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Q: Solve the differential equation by variation of parameters. 4y" - y = ex/2 + 4 y(x) =

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Q: Solve the differential equation by variation of parameters. у" + у %3 csc х y(x)

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Q: (2х + Зу — 5)dx + (3x — у — 2)dy — 0

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Q: yu) + 2y"+ y - x²sinx

A: The given differential equation is: y(4)+2y''+y=x2sin x

Q: μ (x, y)=xayb and find the general solution to the equation

A: Here we have to find out both integrating factor and general solution.

Q: form the differential equation corresponding to (y-b)2=4(x-a)

A: (y-b)2 = 4(x-a)

Q: Find the general solution for the differential equation: 3- y" + 9y = sec2(3x) %3D

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Q: Solve the differential equation by variation of parameteres: y'' + y = csc(x)

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Q: Use separation of variables to find the general solution of the differential equation. 2x dx

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Q: 2ydx = (x2 – 1)(dx – dy)

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Q: Solve the differential equation by undetermined coefficients y" – y' = -3 а.

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Q: Solve the differential equation y" – 2y' + y = ° *| *

A: solve the differential equationy11-2y1+y=exx .....(i)

Q: Solve the differential equation. y' = 4x – y %3D

A: Let v=4x-y Differentiating both sides we get: ddx(v)=ddx(4x-y)v'=4-y'y'=4-v'

Q: Solve the differential equation: xy'-2x2y= y ln y

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Q: Solve for differential equation  (y2-xy)dx+x2dy=0

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) =…

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Q: Use separation of variables to find the general solution of the differential equation. (9 + x)y' =…

A: We have,

Q: Solve the differential equation by undetermined coefficients (annihilator approach). y(4) + y" = 3x2

A: Please see the below picture for detailed solution.

Q: How would you solve the differential equation y'=2t-y using separation of variables to find y(1)?

A: Consider the given differential equation, y'=2t-ydydt+y=2t The above equation cannot be solved by…

Q: Match the differential equation with its solution. y' - 4x'y = x3 %3D

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Q: Solve the differential equation by variation of parameters. y" + y = sin(x) y(x) = %3!

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Q: Solve the differential equation by variation of parameters. 4y"-y = ex/2 + 6 y(x) =

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Q: Solve the differential equation by variation of parameters. 9x y" - 9y = %3D 3x e y(x) =

A: The given differential equation is y"-9y=9xe3x.

Q: Solve the differential equations using method of undetermined coefficient y"+y = x^2sin(2x)

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Q: Solve the Differential Equation using VARIATION OF PARAMETERS: y''-2y'+1=(x+1)e2x

A: The given differential equation is: y''-2y'+y=(x+1)e2x

Q: Find the general solution of the differential equation using any method         y′ = ln(x2 + x)

A: we have to find the solution of the given differential equation  y′ = ln(x2 + x)

Q: x" + 2x' + x = e° -t.

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Q: The differential equation: y²x + y² = x²yy' is solved by

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Q: Solve the differential equation. y' + 3xe" = 0

A: The given differential equation is: y'+3xey=0 To solve the differential equation.

Q: Find the differential equation whose solution is given by y^2=4ax

A: topic - differential equations

Q: Solve the differential equation by an appropriate method. y''+2y'=x^2+4e^2x

A: Given linear differential equations with constant coefficients. We have find General solution for…

Q: Solve the differential equation by undetemined coefficients y" – y' = -3

A: Solution- Given y''-y'=-3 ⇒dy2dx2-dydx=-3-----(1) dydx=m ⇒m2-m=0⇒m(m-1)=0m=0, m-1=0≠m=1 Distinct…

Q: Solve the Homogenous Differential Equation: (x² + y³) = xy ху.

A: This question is based on solution of Homogeneous differential equation.

Q: Find the Differential equation by eliminating the arbitrary constant x2 - y2 = a2

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Q: solve the differential equation xy' - y = 2x ln x

A: Given: xy'-y=2xlnx For finding solution of given differential equation, we convert it in first order…