(10 — 6у + е 32) dx -3x 2dy = 0 -

Q: Solve the given differential equation with initial condition.  y' - .6y = 0, y(0) = 5

A: We have been given the differential equation  y' - .6y = 0 with initial condition y(0) = 5

Q: Solve the given differential equation with initial condition. 7y= 2y', y(0) = 7

A: As the solution statement shows that y is the function of t. So we will proceed accordingly.

Q: 5. y" + 8y + 16y = 0

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Q: The general solution of the differential equation x²y" - 2y = Inx is

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Q: The solution of the differential equation y" + 3y+2.25y = -10e¬1.5x when solved using method of…

A: To uss variation of parameters to find the solution of the given differential equation

Q: Find a particular solution to the differential equation -3y" + 2y' + ly = 2t2 – 2t – 6e*. Yp =

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Q: Find the general solution of the differential equation (D² – 4D+3)y = e*sin3x.

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Q: Find a particular solution to the differential equation y" + 3y' + 2y = -8t³. Yp

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Q: Find general solutions of the differential equation    xyy'=x^2+3y^2

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Q: Solve the given differential equation with initial condition.  y' = 3y, y(0) = 1

A: Given: y' = 3y,  y(0) = 1 To solve: The given differential equation with the given initial…

Q: Find a general solution to the given differential equation. 5z" + 3z' -z = 0

A:

Q: Solve the given differential equation with initial condition. 5y = 3y', y(0) = 7

A: Given: 5y=3y',     y0=7 We can write it as, 5y=3dydx⇒1ydy=53dx Integrate on both sides we get,…

Q: The solution of the differential equation dy dx 6. is 6x + C 6lnx + C | 4 6x + C 5 6lnx + C 2

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Q: 3y" + 2y – ly = 1t² – 1t + 4e¬24 - Yp =

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Q: Find the general solution for the differential equation: 1- y" - 4y = 1+ 65e'cos(2t)

A: Given : y'' - 4y = 1+65et cos(2t)  To find : General solution of the given DE

Q: Find the general solution to the differential equation: y' = 6x + e5z

A:

Q: Find the solution of the given differential equation. x²y-y ; y (3) = -1 %3D y+1

A: Given,dydx=x2y-yy+1,dydx=y(x2-1)y+1y+1ydy=(x2-1)dxTaking integration on both…

Q: Find a particular solution to the differential equation y" + Oz/ – 16y = -768t°.

A: Given: y'' + 0y' - 16y = -768t3

Q: A particular solution of the differential equation y''+3y'+2y=4x+3 is:

A: Solving the differential equation

Q: y" – 3y' + 2y = 3e + 2e2* -

A: Given,y''-3y'+2y=3ex+2e2xNow,Auxillary equation ism2-3m+2=0m2-m-2m+2=0mm-1-2m-1=0m-1m-2=0m=1,2Since…

Q: (6x + y²)dx + y(2x – 3y)dy = 0 -

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Q: Find general solutions of the differential equation    2xy+x^2y'=y^2

A: Given

Q: The general solution of the differential equation y +4y 0 %3D is

A: Topic-  differential equations

Q: . Find the general solution of the given differential equations. y" +y = 0

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Q: Determine the solution to the differential equation given by: y'' + 3y -10y= 0

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Q: Find general solutions of the differential equation          xy+y^2-x^2y'=0

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Q: Find general solutions of the differential equation      3y^2y'+y^3=e^(-x)

A: Consider the provided differential equation,

Q: Find a particular solution to the differential equation Ур || y" + 5y' + 6y=-108t³.

A: Given differential equation is y''+5y'+6y=-108t3 We have to find a particular solution for it.

Q: 5. Find a general solution of the differential equation: y" + 4y' = 2x – 1

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Q: Find a particular solution to the differential equation 4y" + 0y' – ly = -1t² + 2t – 3e4*,

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Q: Find general solutions of the differential equation  x^2y'=xy+3y^2

A: Consider the given: x2y'=xy+3y2 Homogenous equation therefore, substitute y=vx and y'=v+xdvdx.…

Q: solve the second order differential equation ; y''+4y'+5y=8xsinx

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Q: find the general solution of the given differential equation. 5.y″ + 2y′ = 3 + 4 sin(2t)

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Q: (0' +1)- dr +20r =1, given 0=0, r=1 do

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Q: . Solve the given higher order differential equation y" + y' + 2y = 0; y(0) = y'(0) = 0

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Q: Find general solutions of the differential equation       xy^2y'=x^3+y^3

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Q: Find general solutions of the differential equation      2x^2y+x^3y'=1

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Q: Give a general solution of the differential equation y"–9 y = −2t cos 3t

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Q: Compute the value of the constant k for which kx²e5x is a particular solution of the differential…

A: We compute the value of the constant k for which kx2e5x is a particular solution of the differential…

Q: find the general solution of the given differential equation. 2.y″ − y′ − 2y = −2t + 4t2

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Q: find the general solution of the given second-order differential equation.   13-             3y" +…

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Q: Find the complete solution of the differential equation yiv – 2y + 3y" – 2y' + y = 0

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Q: Solve for the particular solution yp of the given differential equation: y" + 3y' + 4y = 4x2 — 2х -

A: Given differential equation, y''+3y'+4y=4x2-2x⇒(D2+3D+4)y=4x2-2x          D≡ddx.............(i)

Q: Find the general solution of the given second-order differential equation. у" + бу' + 9у %3D0 y(x) =

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Q: Find the general solution of the given higher-order differential equation. + 3y" + 3y' + y = 0

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Q: Solve the differential equation dy 3y3 1 dx By the method of separating the variables

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Q: (1+ x)y" + (4x + 5)y' + (4x + 6)y = e-2x

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Q: Find general solutions of the differential equation    3xy^2y'=3x^4+y^3

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Q: Find the general solution of the differential equation (D2- 6D+8)y 11"+ cos 6z

A: The given differential equation is (D2 - 6D + 8)y = 11x + cos(6x) ----(1) The auxiliary equation is…