Find the differential equations having as solution of y = x sin(xtc) .

Q: x + 4y3) dy- ydx = 0

A: We have to find the solution of the given non exact differential equation.

Q: Find the general solution of the differential equation and check the result by differentiation

A: Given differential equation -dydx = 2x-3             ............(1)Separating variables - dy =…

Q: Solve the differential equation using undetermined coefficients method y''+4y=2x sin(x)

A: Given that y''+4y=sin2x Let y=emx Now  m2+4=0m=±2i Therefore the general solution,…

Q: y = C, cos 3x - C sin(-3x)

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Q: Solve the Differential Equation using VARIATION OF PARAMETERS: y''+y'-3y=4sin2x

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: The general solution of the differential equation dz +6y sin 4z is

A: We need to solve the differential equation d2ydx2+6y=sin 4x The solution of this differential…

Q: Find a first order differential equation for which y2 sin(xy) + (2xe)cos(x)) = 3 is an implicit…

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Q: use the method of variation of parameters to find a particular solution of the given differential…

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Q: Determine the solution to the differential equation given by: y'=6y2/x

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Q: solve the differential equations by using integrating factor y'= (y/x) + 2x+1.       when ; y(1)= 3

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Q: Solve the differential equation by variation of parameteres:   y'' + y = sin2 (x)

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Q: Find the complete solution of the differential equation, y' = 2 - cot.

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

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Q: Find the general solution of the differential equation y′ = tan3 3x sec 3x

A: Given: y' = tan3(3x)sec(3x) =>dy/dx = tan3(3x)sec(3x) =>dy = tan3(3x)sec(3x) dx

Q: Find the general solution to the differential equation using undetermined coefficients. y" + 5y =…

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Q: Find a differential equation whose general solution is y = cie®t + cze¬,

A: The complimentary function of the differential equation if the root of the auxiliary equation are…

Q: The differential equation formed by eliminating a and b from y = ae* + be* is

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Q: Find a differential equation whose general solution is y = cjet + cze-". = 0

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Q: Find the differential equation given the general solution: y = cer + Czex + 3x

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Q: 2x + 2xy2 y + 2x²y dy dx ||

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Q: Give a general solution of the differential equation y"+4y=-3 sin 2t.

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Q: Use bernoullis equation to determine the general solution to the differential equation (y^2-y)dx +…

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Q: Find the general solution of the differential equation y′ = √(tan x) sec4 x

A: The function is y'=tan xsec4x. To find the general solution, integrate both sides of the equation.…

Q: The solution of the differential equation y" +y = sin²(t) when solved using method of Variation of…

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Q: Find the solution to the differential equation   that passes through the origin.   z=

A: As the solution function to the given differential equation, passes through the origin we will have:…

Q: (1+x²)(dy-dx)=(2x+arctan² x)dx

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Q: y = Clx+ C2e

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

A: y'' +3y' +2y=12+exA second order linear, non-homogeneous ODE has the form of   ay''+by'+cy=gxThe…

Q: Give the general solution of the differential equation y'-y = sinx + cos2x +e-x

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Q: Solve the 2nd order linear differential equation y" – y' = 5e* – sin2x %3D

A: The auxiallary equation for the given differential equation is given by

Q: use the method of variation of parameters to find a particular solution of the given differential…

A: solution:-  The given differential equation is  y''+4y=cos3x The auxiliary equation of above…

Q: y = 2 -[(1+y(t))sin tdt.

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Q: use the method of variation of parameters to find a particular solution of the given differential…

A: To solve the following differential equation using the method of variation of parameters to find the…

Q: Solve the differential Equation &Y"+y=nsion by using variation of parameter.

A: Given differential equation is ,                                  y" + y =  x sin(x)  Method of…

Q: y' + 2y = cos(2x)

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

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Q: y = ry' – In (y')

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

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Q: Solve the differential equation  by undetermined coefficients. y"+y = 2x sin x

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Q: Find the homogeneous linear differential equation whose solution is y=-e^(3x/2)-4x sin⁡2x.

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Q: Determine the solution to the differential equation given by: y' + 2y = 4 cos x

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Q: The solution of the exact differential equation (ycosx + 2xe") + (sinx + x²ev – 1)y' = 0 is:

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Q: Solve the differential equation using the method of undetermined coefficients. y" - 4y' = sin(3x)

A: Given differential equation is

Q: Find the solution of differential equation 4º+y = sin dx2

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Q: b. y = C, + Cze3*

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Q: Solve the differential equation by the method of variation of parameters. y"+3y'+2y=1/(1+ex)

A: The differential equation is given by,

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