G(m1+m2) 1) +y de h2 This is an oscillating differential equation. So the answer to this equation would be : G(m1+m2) 2) y + acose = h? Prove Equation 1 to arrive at Equation 2

Q: determine the general solution to thegiven differential equation. y′′ + 8y′ + 20y = 0.

A:

Q: Show that the y,(2) = K, (1 – 2x* +*-*-)* * (2x -+ 4 x6 + ... 45 4 + K2 (2x 4 8 + ... 3 15 315 is…

A: we have given yh(x)=k11-2x2+23x4-445x6+...+k22x-43x3+415x5-...is complementary solution of…

Q: The auxiliary equation for the differential equation y" – 4y" – 12y = 0 - is

A: The given problem can be solved as follows:

Q: determine the general solution to thegiven differential equation. y′′ + 10y′ + 25y = 0.

A: To determine the general solution of the given differential equation.

Q: Find the solution of the differential equation which satisfies the indicated conditions: 1. y" – 3y'…

A:

Q: (D² – 3D + 2) y = (1+e-*)?

A:

Q: Solve the Second order differential equation: y" + 7y' + 12y = 0

A:

Q: Determine whether or not y=C1 cos (2t) + C2 sin (2t) is the solution to the differential equation…

A: we check y=c1 cos(2t)+c2sin92t) is the solution to the differential equation y''+4y=0

Q: The complete solution to the nonhomogeneous differential equation (D^3 +D- 10)y = 116e^(4x), is %3D

A: Solution

Q: Obtain the solution of the following differential equations. 3. (16x + 5y)dx + (3x + y)dy = 0 ; the…

A:

Q: What will be the order of differential equation if its solution is y = C,sinx+ Cze O a. None of…

A: To find the order of the differential equation if it's solution is: y=c1sinx+c2e−x

Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''-4y-12y=e6t

A:

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: What is the complementary solution y, for the differential equation y"- 4y=12x A y,=c,cos 2x + c,sin…

A:

Q: Find the solution to the differential equation below such that y(0) = 8 y' = 8xy – 2x y(æ) =

A:

Q: Suppose the roots of the auxiliary equation are at iß. These are unequal roots, the general solution…

A:

Q: equation, 3(x^2 + y^2)dx + x(x^2 + 3y^2 + 6y)dy = 0, what is the solution to the differential…

A:

Q: | The equation 6y' – 2y = xy is a separable differential equation. True

A:

Q: (a) y = Ae + Be+Ccos 2x + Dsin 2x

A:

Q: Show that if the roots of the auxiliary equation of a differential equation are r = p± qi, then the…

A: The given roots are r=p±qi. Show that the differential equation itself is y''-2py'+p2+q2y=0. Here we…

Q: Verify that y = c, sin 3x + c2 cos 3x + 4e* is a solution to the differential equation y"-y" + 3y'-…

A: We have to verify that, y = c_1 sin 3x + c_2 cos 3x + 4e^x ;  is a solution to the differential…

Q: Find the solution to the differential equation below such that y(0) = 8 y' = 8xy – 2x - y(x) =

A: Given: y'=8xy-2x    , y(0)=8 Taking y'=8xy-2x ⇒y'-8xy=-2x To make calculation easy multiply both…

Q: (b)Verify that the differential equation y = 2 sin 2x is a solution y" + 4y = 0

A:

Q: y!V – y"'+ 2y' = 0

A:

Q: The particular solution of the following nonhomogeneous differential equation y" – 6y' + 9y = 4x? +…

A: given differential equation  y''-6y'+9y=4x2+e3x claim- form of particular solution using method of…

Q: The auxiliary equation for the differential equation xy" + 3xy'+y= 6 is

A:

Q: The solution of the differential equation + 2y = a is, Oy = +c Oy= Oy = Oy= T

A: The objective is to find the solution of the differential equation.

Q: The degree of the differential equation (y") +y' – y = x is а. 2 с. 1 h no decree

A: We are asked to find the degree of the differential equation.

Q: Determine the general solution to thegiven differential equation. (D + 2)2 y = 0.

A:

Q: (i+ y? tXy?) dr t (x?y ty +2xy) dy

A:

Q: The complete solution to the nonhomogeneous differential equation (D^3 + D - 10)y = 116e^(4x), is *

A: Explanation of the answer is as follows

Q: What is the general solution of the first order differential equation a csc (2) – B da + a dß = 0 if…

A:

Q: Find a particular solution to the nonhomogeneous differential equation: +(y" + 4y' + 5y = 15x +…

A: The given differential equation is y''+4y'+5y=15x+3e-x To find the particular solution let the trial…

Q: The suitable form of the differential equation y" + 2y'-3y = 5e2t, is Y = Aje2t, then the value of…

A:

Q: The dependent variable y is missing in the given differential equation. Solve the equation by the…

A:

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

A:

Q: a) (2² - 1)v = y² – 1, yı (2) = 1

A:

Q: y = cje* + cze²r y" -y – 2y = 0 O 2y " -y' – y = 0

A:

Q: The particular solution of the following nonhomogeneous differential equation y" - 2y' +y = 4x? + e*…

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

Q: determine the general solution to thegiven differential equation y(iv) − 16y = 0.

A: Determine the generalsolution of given differential equation. yiv-16y=0

Q: What is the general solution of the first order differential equation a csc (2) – B da + a dß = 0 if…

A:

Q: The solution of the differential equation: y" - 4y +4y = e2x when solved using method of…

A: Given DE is y”-4y’+4y=e2x solve the given equation

Q: Find the solution to the differential equation below such that y(0) = 14 y' = 10xy - 2x y(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2. Solve the nonhomogeneous differential equation, using the basic rule: y(2) + 6y(?) + 9y =…

A:

Q: Determine the general solution to thegiven differential equation. y′′ − 6y′ + 9y = 0.

A: From the given data:

Q: Solve the second order differential equation ÿ + ỷ – 6y = 8e* + 3x 1 A:y = ce2x + c2e-3x + 2e* + 12…

A:

Q: The complete solution to the nonhomogeneous differential equation, (D^2 +D - 6)y = 2x, is *

A:

Q: (b). By reversing the role of x and yY or otherwise, find the general solution to the differential…

A: Given:        2x-4y2dydx+y=0            2x-4y2dy+ydx=0    Equation in total differentials:…

Q: Find a general solution of the differential equation: у" — 4y" — Зу' + 18у %3D Зе* -

A: see the attachments

Q: A/ find solution for the differential equation below: Y"' - 6Y" + 11Y – 6 = 0

A: