Given the differential equation (y² – 2xe") dz + (2xy – z²e") dy = 0 8M ? ,What is бу | 2y – 2ey -2xey • 2y – 2xey O-2x

Q: 2. Show that y = e-6t satisfies the differential equation y" – y – 42y = 0.

A: We have to verify that y''-y'-42y=0 when y=e-6t. We know that d2ydt2=y''dydt=y'de-atdt=-ae-at So…

Q: 3. y" - 2y" - у' + 2у %3D е4x + х2 +1

A:

Q: 5x y = C, + C2e4x 4

A:

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

A: The given differential equation is

Q: Show that the differential equation  (2xy3 - 3y2 + 2xy2)dx + (3x2y2 - 6xy + 2x2y)dy = 0 is exact and…

A: To show that the differential equation  2xy3-3y2+2xy2dx+3x2y2-6xy+2x2ydy=0 is exact and to find its…

Q: Find the differential equation of the cubics : cy^2= x^2 ( x - a ) with a held fixed.

A: Here c is arbitrary constant and a  is fixed. So we have to find a differential equation which does…

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

A: To solve:

Q: Find the general solution of the first order differential equation (x+2) y′ + 4y = (3x + 6)-2 lnx.

A: Given: x+2y'+4y=3x+6-2lnx for finding solution of given differential equation, first we convert it…

Q: The differential equation formed by eliminating arbitrary constants a and 6: y = ax + bx+9 is

A: Given that

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

A: Solution

Q: Determine the form of a particular solution to the nonhomogeneous differential equation by the…

A:

Q: use the method of variation of parameters to determine the general solution of the given…

A:

Q: Find the general solution of the first-order linear differential equation. 8y xy = x-2

A:

Q: The general solution of the differential equation x2y′′+xy′+(25x2−9)y=0x2y′′+xy′+(25x2−9)y=0 is?

A: The differential equation of the form  x2y''+xy'+x2-ν2y=0            i is referred to as Bessel's…

Q: 8. Consider the homogeneous linear equation: 2.a²y" + 3xy' – y = 0, x > 0. (a) Explain why y = e" is…

A: Note: Since these are independent subparts, according to our policy we are only allowed to solve…

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

A: 2x2y-x3y'=y3 We need to find the general solutions of the differential equation.

Q: Find the solution of the Linear Homogenous Differential Equation with Constant Cofficients. (2D4 +…

A:

Q: Find the solution to the Cauchy-Euler differential equation xy' +3y'+y=0.

A: The Cauchy-Euler differential equation of second order can be written in the form:…

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

A: Given

Q: What is the general solution to the differential equation (3x+2y+4)dx+(3x+2y-3)dy=0?

A: An equation which involves the derivative or differential coefficient is called differential…

Q: 2. Solve the nonhomogeneous differential equation, using the basic rule: y(2) + 6y(1) + 9y =…

A:

Q: y" – 5y' + 6y = -3Sin (2x)

A:

Q: y" – 4y' + 4y = 2x

A:

Q: The integrating factor of the differential equation 2xy dx + (4y + 3x^2) dy = 0 is . Does not exist

A: Ist question was incomplete I have to do the second question Please repost ist question correctly

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 solution of the differential equation of (2x° + ry? + 2y +3) dr + (x²y + 2x) dy = 0 ?

A: We have given differential equation,   Differential equation is of the form,     Mdx +Ndy=0 Firstly…

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: Suppose dr - =4sin(2x) and y= -2 when *=. what is the particular solution to the given differential…

A: In this question, we need to find the particular solution to the given differential equation.

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

A:

Q: Solve the differential equation with initial conditions y" - 3y 10y = 4e5t y(0) = 0, y' (0) = 1…

A:

Q: Find the homogeneous differential equation whose general solution is y = 3cos(x) - e3x/2 -…

A: Given the solution of a homogeneous differential equation   y = 3cos(x) - e3x/2 - 4xsin(2x) Find the…

Q: In the differential equation (2x+3y-5)dx+(3x- y-2)dy=0, the lines 2x+3y-5 =0 and 3x- y-2 =0…

A: This question can be solved using the concept of solving two linear equation.

Q: Match the differential equation with its solution. y' - 4x'y = x3 %3D

A:

Q: What is the particular solution of the differential equation determined by the initial conditions,…

A: In the question we have to find the particular solution.

Q: 6, find the general solution of the given differential equation: y" - 5y + 4y = 2et (

A:

Q: is a solution of the differential equation y" + (3x + 1)y' + 3y = 0 , then its coefficients Cn are…

A:

Q: By the alimination of the arbitary constants a and b ,obtain the differential equation of which…

A: Given solution is xy=aex+be-x+x2 find DE by eliminating arbitrary constants

Q: Find the general solution of the first-order linear differential equation y′ + 3x2y = 6x2 for x >…

A: Given: The first-order linear differential equation: y'+3x2y=6x2 for x>0.

Q: Given the differential equation 4ry + 6x) dr + (r³ – 6x²y² – 1) dy = 0 ,What is (3z y 6M by %3D -- O…

A: Given:       3x2y-4xy3+6xdx+x3-6x2y2-1dy=0 Here M=3x2y-4xy3+6x            N=x3-6x2y2-1

Q: Determine the solutions of the 1st-order linear differential equations below 3x2y′ = 2y(y −3)

A: Use separable variable method

Q: Calculate the particular solution to the forced differential equation x" + 3x = 5cos(2t)

A:

Q: What is the particular solution of the differential equation y" + 2y" – 5y' – 6y = 5e?? Particular…

A:

Q: Determine the solution of the differential equation у"+2y" - 5y - бу%3D0 that has values y= 3, y = 6…

A: The differential equation y'''+2y''-5y'-6y=0 where y0=3,y'0=6,y''0=12. Rewrite the equation using…

Q: Find the general solution of differential equation, and when initial conditios are given, the…

A:

Q: What are two linearly independentsolutions of the differential equation y''-5y'-6y=0

A: We have to find linearly independent solutions of the given differential equation.

Q: Show that y1 =- and y2 = Vx are solutions of the following differential equation 4x3у" + 7x?у' — ху…

A: According to the given information, it is required to show that the given y1 and y2 are the…

Q: The General solution of the differential equation 3x2 + 2x + 6 is x3 + x2 + 6x dy using variable…

A:

Q: Form the differential equation if its solution is y=acos2x+bsin2x a. y"+4y=0 b. y" – 4y = 0 c.…

A:

Q: Consider the differential equation (10x³y* + e=y + 3 sin(4x + 3y))y' + (6x²y5 + 4 sin(4x + 3y) + 2)…

A: