(3) y" – 25y = 2xe"

Q: Solve the initial-value problem using the method of undetermined coefficients. y" + 5y' – 6y = 8e2x;…

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Q: Find the general solution valid near x=0 (x2 + 4) y" + 2xy' -12y = 0

A: We have to solve given problem:

Q: ) Solve the initial-value problem dy :-2y 2x* ;y(2) = 8 %3D x- dx

A: We have to solve the given differential equation using the initial condition. Rearranging the…

Q: A. Find the general solution of the DE: y" - 2y' +y = 6e'

A: Given A. y"-2y'+y=6et

Q: Find the general solution of dy -2x6 dx y-4

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Q: Solve the initial value problem using the method of undetermined coefficients.  y"+4y'+4y=(3+x)e-2x,…

A: The given intial value problem is given by,

Q: Find the solution satisfying the initial conditions: y" - y = x2 y(0) = 0 y'(0) = -1

A: Given that: y''-y=x2

Q: 3. Solve Bernoulli equation: xy' = y + y³

A: The differential equation is given as xy'=y+y3 It can be rewritten as…

Q: Obtain the general solution. xy3dx+ex^2dy=0

A: The given differential equation is xy3dx+ex2dy=0. We have to obtain a general solution.

Q: find the general solution of the given equation. 3y'' - y' = 0

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Q: Find the general solution of y’ + (1/3)y = exy4

A: We have to find the general solution of the differential equation y'+13y=exy4 .

Q: Find a general solution valid near the origin: (x²+4)y" + 2xy' - 12y = 0

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Q: -1:B: Solve the initial value problem : * d²y + 4y = 8x2 ,y(0) = -3,y'(0) = 0 dx2

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Q: y′−6x=5+2y y(0)=−3 Is y=e2x −3x−4 a solution to the initial value problem shown above?

A: The given differential equation is y′−6x=5+2y.The solution of the deferential equation is given as,…

Q: Find the general Solution of DES: x yy'= x +3y

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Q: Find a general solution of y"- 2iy'+3y= 0.

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Q: Find the solution of the initial value problem. 2y" - Зу' + у%3D0, у(0) %3D 2, y'(0) =

A: Here first we write an auxiliary equation of a given differential equation then  finding roots of…

Q: yV + 2y" + y" = re=*

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Q: (2 marks) The general solution of the 3y = 0 equation (6xy + e')y' + xe* + is

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Q: Find the general solution to y" – xy' = 0. -

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Q: Find the solution of the initial-value problem dy + 3r*y = x², y(0) = 2. %3D dr

A: First order differential equation of the form ; are known as Leibni'z linear equation. The solution…

Q: Find the general solution of (xy² + x²)dy + a. 3xy + y3 = C b. 3xy - y3 = C xydx = 0 с. -Зху - уз с…

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Q: 6. Find a general solution to the third order equation y" + y" + 3y – 5y = 0.

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Q: Find a particular solution for: y" - 3y' + 2y = te*

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Q: 12. Find the general solution of x²dx + y(x – 1)dy = 0

A: This is a variable seperable DE.

Q: Q1: Solve the second order linear homogenous equation: y" – 2ky' + 4y = 0 k > 2 -

A: According to our guideline we can only answer first question and rest can be reposted.

Q: 3. Solve y' = , with initial condition y(1) = 0. y2 – 1 x3

A: It is given that the differential equation dydx=y2-1x3. Using variable and separable method to…

Q: Is y=e3x−2x−3 a solution to the initial value problem shown below? y′−3y=6x+7 y(0)=−2   Yes or no?

A: Yes

Q: dy 3. Solve dx = -8xy² +4x(4x+1)y-(8x' +4x² -1) by knowing u = x is a solution.

A: Given differential equation is dydx=-8xy2+4x4x+1y-8x3+4x2-1             …(1) y=x is a solution of…

Q: 2. Solve y' = 2x(x² – y), with initial condition y(0) = 1. -

A: This is first order linear differential equation

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

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Q: Find the general Solution of DES x y = xy +y

A: Given:    x2y' = xy + y2

Q: Find the general solution of the given DE. y"-2y"-y'+ 2y 0 %D

A: NOTE: Refresh your page if you can't see any equations. . the auxiliary equation is given by

Q: -4x e Find a particular solution to y" + 8y' + 16y= x3

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Q: 4. Solve the IVP y' = 2x-3y +e¯* y'= 2x- 3 y +e * with y(0) = 1 y(0)= 1

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Q: Find the general solution to: 3X y^ - Gy' +Qy= x*e*

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Q: Find the general solution of (2x – y) dy = 2y – x - da

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Q: Solve the Bernoulli Equation xyy' + y² = 2x

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Q: 2. Find the general solution of y' = eY(4x – 2). %3D |

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Q: ) Find the general solution of the DE y = (2+y')x+ (y')².

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Q: The general solution of the DE y"-y" + y'- y=0 is

A: We need to factorize this equation to find the solution.

Q: Solve the initial value problem using y"+3y'+ 2y = 2u(t-2).y(0) = 0, y (0) = 0

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Q: Solve y' = 6x, x' = x + y with initial conditions x(0) = 1, y(0) = -2.

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Q: Solve the Bernoulli Equation xyy + y² = 2x

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Q: Find the general solution of the DE below. y(1) + y “ + y“ = 0 יינ

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Q: The general solution of the DE y" -y" + y'-y 0 is

A: we have to find out the general solution of the differencial equation y'''-y''+y'-1=0

Q: Find the general solution of y" + 2y=ex +2.

A: The Auxiliary equation is D2+2=0 solve for D Therefore  D=±-2=±2i Therefore the solution is…

Q: 1 Find the general solution of x'y" +xy' -y= x+1

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Q: Find the general solution of D² + 16D)y = cos4x

A: We have to find general solution of the differential equation: D2+16Dy=cos4x Auxiliary equation…