Solve the differential equation by variation of parameters. y"+ y = sin(x) %3D x cos(x) y(x) = c,cos(x) + c,sin (x) - %3D 2

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Q: Solve the differential equation explicitly for y(x) and find the domain of the solution: 4xy2 +…

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Q: solve the differential equation y′′ + y = 4 cos(t)

A: solve the differential equation y′′ + y =4cos(t)

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A: The general solution of a differential equation always contains a constant of integration. The…

Q: Solve the Cauchy-Euler differential equation x -2x+2y = x dx dx

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Q: solve the differential equation (2x+y cos(xy))dx+x cos(xy)dy=0

A: Solution:                    The given differential equation is                   2x+y cos…

Q: Solve the differential equation. (y + Sin y) y'   =  x + x3

A: Write the equation in terms of differentials and integrate on both sides as follows.

Q: Solve the differential equation + cos(x+ y)+2x]dx+[xe' +cos(x+ y)-1]dy = 0

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Q: Solve the differential equation 1.) dy = (y²xe^3-3x²y)dx

A: Please see the below picture for detailed solution.

Q: sin y(x + sin y)dx + 2x cos ydy = 0

A: Given: sinyx+sinydx+2x2cosy dy=0Bernoulli's equation:dydx+pxy=qxynLet v=y1-nLinear differential…

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Q: Solve the differential equation y" - 3y +2y cos(e-*)

A: This is a Non-linear differential equation. Which I have solved by operator method. See the solution…

Q: y"- by! + gy = e

A: We have to solve the differential equation…

Q: 2ydx = (x2 – 1)(dx – dy)

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Q: Find the solution of the differential equation? (sin x + tan-1 )) dx = (y – In/x² + y² ) dy

A: Consider the differential equation, sinx+tan-1yxdx=y-lnx2+y2dy On re-arranging the equation becomes…

Q: Solve the differential equation by variation of parameters. 2y" - 4y' + 4y = e* sec x

A: The objective is to solve the differential equation by variation of parameters 2y''-4y'+4y=ex sec x

Q: Solve the differential equation 4y® ,6 dy 7xe-y' sin x? = 0 dx -

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Q: solve the differential equation y′′ + y = 4 cos(2t)

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Q: Solve the differential equation y"-9 y+20 y= sin(x)--'cos(x)¶

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Q: solve the differential equation using Bernoulli. xydx+(x2-3y)dy=0

A: Given differential equation is  xydx+x2-3ydy=0 which can be written as…

Q: Solve the differential equation y""+y" = 3x² + sin x - 2 cos x What is the particular solution?

A: We have to find the particular solution.

Q: Solve the differential equation by variation of parameters. y" + 3y' + 2y = cos(e*) y(x) =

A: Given differential equation: y''+3y'+2y=cosex               ...(1) Write the homogenous equation…

Q: Solve the differential equation y" - 3y+2y cos(e-x)

A: A solution of a differential equation is an expression for the dependent variable in terms of the…

Q: Solve the first order differential equation. (3x - y - 4)dy - (x + y - 4)dx = 0

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Q: Solve the first order differential equation. dy - y ln(y ecos x) dx = y sin xdx

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Q: Solve the differential equation by variation of parameters. 16х у" - 16у %3D 4x e У(x) %3

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Q: Solve the differential equation  y′′ + 9y = 9x - cos 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 given differential equation by separation of variables. e-y + e-5x - y exy dy dx

A: To find the solution of D.E.

Q: Solve the differential equation y ' = 2 sin x cos x

A: Given the differential equation as Use the 2A formula from trigonometry which states

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

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Q: Solve the differential equation cos(x + y) dx + (3y² + 2y + cos(x + y)) dy = 0. f (y). Express your…

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Q: Find the general solution to the non-homogeneous differential equation. y" - 3y' = sin(3x)

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Q: Solve the differential equation y"" + y = 3x² + sin x - 2 cos x

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Q: Solve the differential equation of dx (A) In y = c Inx

A: Given: dydx=ylnx

Q: Solve the differential equation dy/dx =(3x^2 - sin⁡ y)/x cos y.

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Q: Solve the first order differential equation to find the particular solution. (cos x) + y sin x = 2x…

A: To solve the given differential equation.

Q: Solve the differential equations y' + (tan x) y = cos2 x, -π/2 < x < π/2

A: we have to solve the differential equation  y' + (tan x) y = cos2 x, -π/2 < x < π/2

Q: Solve the differential equation: y' = cos2(x)cos2(2y)

A: Here we solve the differential equationY'=cos2x cos22y

Q: Solve the differential equation (D² +1) y = x² cos 5x

A: Solution :-

Q: dy 1 ху + dx ' 1- x2 = xy2 ху2

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Q: )(I + cos x) y Sin?x + Sin? x cos x -y sinx

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Q: Solve the fourth order differential equation completely d*y d°(y/x) - = sin(x)+cos(x) dx* dx³

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Q: Solve the differential equation by an appropriate method. d³y, dy dx3 tanx dx

A: Find the complementary function and particular Integral of the given equation. Its general solution…