Solve the given differential equation by separation of variables. dy exy e-Y + e-4x - y xp

Q: dy 2x + (4x + y – 6) = y dx

A: The solution is given below in the next step:

Q: solve the given differential equation. y − xdy/dx = 3 − 2x2 dy/dx

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Q: Solve the given differential equation by undetermined coefficients. y" - y' - 30y = e6x y(x) =

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Q: y? dx + (x + 3ay + 4y) dy = 0

A: It is a homogeneous differential equation. Find dxdyand Substitute x=vy.

Q: Find the differential equation whose solution is given by y? = 4ax ydx – 2xdy = 0 O ydy – 2xdx = 0

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 8ex - 6 y(x) =

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 12e - 3 y(x) =

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Q: Solve the given differential equation by variation of parameters. xy" – 8y' = x8 | y(x) = ,x > 0

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y'- 3y = 8ex - 3 y(x) =

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Q: dy +3y = 3x²e-3x dx

A: It ia Linear differential equation.

Q: Solve the given differential equation by undetermined coefficients. y"- 2y'- 3y = 12e- 3 %3D

A: The second order linear non- homogeneous ordinary differential equation is of the form…

Q: Solve the given differential equation by separation of variables. xy + 6y-x6 dy xy - 7y + x - 7

A: Given dydx = xy + 6y - x - 6xy - 7y + x - 7

Q: Solve the given differential equation by undetermined coefficients. y" - 2y' 3y = 12ex - 12 y(x) =

A: See  the details solution in below

Q: Solve the given differential equation by undetermined coefficients. (1/4)y'' + y' + y = x2 − 5x

A: Consider the differential equation 14y''+y'+y=x2−5x We have solve the given differential equation by…

Q: Solve the given differential equation by separation of variables. dy ху + 5х — у - 5 dx ху — 2х + бу…

A: The solution of the provided differential equation by separation of variables is given by,

Q: Solve the given differential equation (3x-3y-2) da – (x – y+ 1) dy = 0 %3D | |

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Q: Solve the given differential equation. y'+2x*y=6y°x*

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Q: Solve the given differential equation. x?y" + xy' + 36y = 0 y(x) : ,x > 0

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Q: solve the given differential equation 6. dy/dx=x^2(1+y^2)

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Q: Solve the given differential equation. dy a. dx (2y+3\² 4x+5,

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Q: Solve the given differential equation. dx 4y² + 6xy dy 3y² + 2x

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Q: Solve the given differential equation by separation of variables. dy xy + 5x - y - 5 dx xy - 2x + 6y…

A: We can solve the given differential equation by using the variable separable method.

Q: Solve the given differential equation by separation of variables. dy = e5x + 4y dx -4e5x 5 + C X

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Q: Solve the given differential equation. 25x?y" + 25xy' + y = 0 y(x) = ,x > 0 %3D

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

Q: Solve the given differential equation. x?y" - 12y = 0 +V7 Y(x) =

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Q: Solve the given differential equation by separation of variables. dy 2y + 7\2 dx 8x + 9

A: If the differential equation can be written in the form of fydy=gxdx then it is called separable…

Q: solve the given differential equation. dy/dx = 2x(y − 1)/(x2 + 3)

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Q: dy Solve the given differential equation by separation of variables: x- = 4y dæ y = ÷a³ +c Oy = || =…

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' 3y = 4ex - 12 y(x) =…

A: The given differential equation is.; y''-2y'-3y=4ex-12.

Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 8ex - 6 y(x) = =

A: Consider the given differential equation, y''-2y'-3y=8ex-6 The auxiliary equation will be,…

Q: Solve the given differential equation. x?y" + xy' + 4y = o

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Q: Solve the given differential equation. 1. (y? + 1)dx – ysec?x dy = 0

A: The given differential equation is,  y2+1dx-ysec2xdy=0

Q: Solve the given differential equation. (x² + 9) dy = (2x − 8xy) dx

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 4ex - 3 y(x) =

A: We need to solve D.E.

Q: Solve the given differential equation by undetermined coefficients. y" - 8y' + 20y = 100x2 – 78xe*…

A: First determine the auxiliary equation to get the complementary function. Now for particular…

Q: Solve the given differential equation by separation of variables. (ey+1)2e-ydx+(ex+1)6e-xdy=0

A: Rearranging the given equation:

Q: Solve the given differential equation by separation of variables. dx + exdy = 0 y = 14e - 4x + C X

A: We can solve the given differential equation by using the variable separable method

Q: Solve the given differential equation by undetermined coefficients. y" – y' – 12y = e4x %3D y(x)

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Q: dy – y = e*y? dx

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Solve the given differential equation (4x + y- 1) da + (x - y- 4) dy = 0

A: To solve the differential equation.

Q: Solve the given differential equation by separation of variables. dy xV1- y2 %3D xp

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Q: Solve the given differential equation. (y² + 5) dx = y sec²(x) dy

A: For the given differential Equation (y2+5)dx=ysec2(x)dy is  y=cex+cosxsinx-5 , y=-cex+cosxsinx-5

Q: Solve the given differential equation.  dy/dx=x5y2

A: Given : dydx = x5y2

Q: Solve the given differential equation by separation of variables. dy xy + 6y-x-6 = dx xy-7y+x-7

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Q: Solve the given differential equation by undetermined coefficients. y" + 6y' + 5y = 10 y(x) =

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Q: Solve the given differential equation (4x+y-1) da + (x - y – 4) dy= 0

A: We have to solve the given differential equation.

Q: (2y+3 dy a. dx 14. 4x+5/

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Q: x²y" – 2y = 0

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Q: (rcsc - y) dr + ady = 0 =D0

A: We will solve the problem