Solve the second-order equation xy" + 2y' 8x? by making the substitution u -y'.

Q: Obtain the differential equations satisfied by the given particular solution 2. y = 7- 2x +e*

A: The objective of the question is determine the differential equation.   Note -  As per our…

Q: Solve the differential equation y'=(3x+3y-1)^2. Use the substitution u=3x+3y-1

A: The given differential equation is

Q: Solve the differential equations using the substitution suggested by the equation. (2x + y)dx -3(2x…

A:

Q: Use the method of undetermined coefficients to solve the differential equa- -2x y" + 5y' + 6y = e-®…

A:

Q: Obtain the differential equation whose general solution is y =a sin 6x- bcos 6z, where a and b are

A: Given: y=asin6x-bcos6x for finding differential equation for given equation, we have to eliminate a…

Q: Verify that the function y = 2x - 6x + 10 satisfies the differential equation -y"-xy"-2y' = -24x.…

A:

Q: y" – 2y – 3y = 2e² – 10 sin z

A:

Q: Find a particular solution to the differential equation using the Method of Undetermined…

A: Consider the given differential equation,

Q: у" — 8y 3D 0, у(0) %3D 4, у'(0) %3D5 and y"(0) —D 7

A: We have to solve

Q: solve the differential equatior y"-8y'+16y=O

A:

Q: Solve the differential equations using the substitution suggested by the equation. (x + 2y - 1)dx +…

A: Given the differential equation is (x + 2y - 1) dx + (2x + 4y - 3) dy = 0; when x = 2 and y = -1.

Q: Solve the differential equation by variation of parameters. 4y" - 8y' + 8y %3D еx sec x y(x) =

A: The solution for the asked question is given as

Q: Solve the differential equation by variation of parameters. 1 y' + 3y' + 2y 6+e*

A:

Q: Find a particular solution to the differential equation using the Method of Undetermined…

A: Given that  The differentiatal equation  To find the particular solution by using the undetermined…

Q: Solve the differential equation y" – 4y' + 4y = %3D -

A: Given that a differential equation : y" - 4y' + 4y = e2x/x.  Here i attached solution of this…

Q: y" + 25y = 0, y(0) = 4.6, y'(0) = -1.2

A:

Q: Solve the differential equation by variation of parameters. 1 y" + 3y' + 2y 9 + e*

A:

Q: Solve the differential equaton 2x2dy=(x+y)2dx

A:

Q: Solve the Differential Equation using VARIATION OF PARAMETERS: 2y''+18y=6tan(3t)

A:

Q: 2. (x +1)y'+y = x² – 1 %3D -

A: Topic = Differential equation

Q: Give the differential equation that has as its general solution. y = C₁ sin(2x + C₂)

A:

Q: dy 2x dx = 3xy + y? ;y(1) =-2

A: dydx = 3xy+y22x2

Q: a. y = C,e=x + Cze-2x + x

A:

Q: The characteristic roots in the differential equation (4D^4 + 4D^3 - 3D^2 - 2D + 1)y = 0 are all…

A:

Q: Use the procedures developed in this chapter to find the general solution of the differential…

A:

Q: Solve the differential equation by the method of integrating factors.

A:

Q: Solve the differential equation by undetermined coefficients: 4y" – 4y' – 3y = cos 2x. |

A: 4y''-4y'-3y=cos 2xGeneral solution:y=yc+ypFor yc4y''-4y'-3y=0Auxiliary equation:4m2-4m-3=0m=4±16+488…

Q: Find a differential equation whose general solution is y = c₁et + c₂e-4t . = 0

A:

Q: Solve the differential equation by variation of parameters. y" + 3y + 2y = 8 1

A:

Q: Solve the given differential equation by undetermined coefficients. y" + 5y = -180x2e5x Y(x) =…

A:

Q: Obtain the roots and the factored operator form linear differential equations y = x2 – 5 sin 3x

A:

Q: Solve the differential Egueations Zydx - (3xy*dx- xdy =0 When

A:

Q: y(4) 4х + 2хе %3D

A:

Q: Solve the given third-order differential equation by variation of parameters. у" - бу" — у'+ бу 3D…

A:

Q: y = Ax² + Be*

A:

Q: Find the solution of the differential equation using inverse differential operation y'' + 6y' + 13y…

A: We have to find the solution of the differential equation y''+6y'+13y=7e-x+26 by using inverse…

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

A:

Q: -3z y" + 6y' + 9y = for a> 0.

A:

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

A:

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 equa 5. y' = 2x?y – 4y %3D

A: The solution for the asked question is given as

Q: Find the terminal value, lim y (r), for the solution of differential equation dy + 3z'y - 6z". dr

A:

Q: - ydx + (x++ xy )dy = 0

A: Differential Equation:- A differential equation is an equation that relates one or more unknown…

Q: Solve the differential equation by variation of parameters. 3y" 6y' + 6y = ex sec x y(x) =

A: Given :  A differential equation 3y''-6y'+6y=ex secx. To find : The solution of a differential…

Q: Solve the Euler-Cauchy differential equation dy - 3x +4 y = In ² x – In x xp dx

A:

Q: Solve the differential equation by undetermined coefficients: y" + y – 6y = 2.x.

A:

Q: Solve the differential equatons (9xy-2y2) dx - ( 6x²_xy) dy =0 4.

A:

Q: (2x+ykdx– 3(2x+ y+4)dy=0 1.

A: Note: We are required to answer only the first question, unless specified.

Q: Find a differential equation whose general solution is 6t y = c₁et + c₂e -3t = 0

A: We find a differential equation whose general solution is y=c1e6t+c2e-3t.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.