Find the general solution of the following: 1. (4D? – 4D + 1)y = 0 3. (4D? – 6D + 1)y = 0

Q: Solve the following : x2 + y2 + 3y =22 2x + y =-1

A: To solve the given equations.

Q: Q1: Write down the form of the particular solution of: y(5). 3y(4).y(2)+3y(1) = x² + xe *

A: The given differential equation is: y(5)-3y(4)-y(2)+3y(1)=x2+xex

Q: Find the general solution of (29) y′′+9y=0.

A:

Q: Given that x = 3 is a solution to 2tx - y = 4, what is the value of 12t - 2y?

A:

Q: What is the general solution to: y''' - 4y'' = 0

A: Given y"'-4y''=0

Q: Find the general solution of the following: 11.(D² – 2D + 5)y = 0

A:

Q: Find the general solution of (D² - 5D + 6)y = 4eˉˣ

A: Given: The equation is D2 - 5D + 6y = 4e-x.

Q: Find the general solution: (x^2D^2 + 6xD + 6I)y = x^2

A: Find the general solution: (x^2D^2 + 6xD + 6I)y = x^2 Given D.E., x2D2+6xD+6)y=x2⋯(1) which is…

Q: Find the general solution of the Following problem? y" + 4y' + 6y = 0

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Q: What is the solution of the given equation valid near the origin for x>0? x2y''+x(2+3x)y'-2y=0

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Q: Find the general solution of the following IVP: y"- 2y' +y = 0 ,y(0) = 5, y'(0) = 10.

A:

Q: dy = 6x(y – 1)2/3. dr

A:

Q: Find the general solution of the following 14.(D² – D + 1)y = 0

A:

Q: Find the general solution of the Following problem? y" - 2y' - 3y = 0

A: y''-2y'-3y=0 Auxiliary equation       m2-2m-3=0 =>m2-3m+m-3=0 =>m(m-3)+1(m-3)=0…

Q: r²y" + 3ry' + y = In(z)+1 z((In(z))²+1)

A: The given differential equation x2y''+3xy'+y=ln(x)+1x((ln(x))2+1) is a homogeneous linear equation.…

Q: Find the general solution to y" – y' – 2y = 3x + 4. (Be sure to find the values of the coefficients…

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Q: Solve the following equation for r. V2 73- 4

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Q: Find the general solution of the following 17. (D² + 49)²y = 0

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Q: The general solution to y" – 2ay' +y = 0 is given by

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Q: Solve the following equations  by the method of undeterminedcoefficients. y" + 2y' + y = x2

A: The given differential equation is y''+2y'+y=x2. Auxiliary equation of homogenous system is…

Q: Find the general solution of the Following problem? 16y" - 24y' + 9y = 0

A: Given:16y"-24y'+9y=0

Q: Q2 :Given that the equation x² – kx + 8 = 0 where k ER has one of the solutions is %3D x = 2 - j2.…

A:

Q: Find the general solution of the following equation * + 5 + 6y = 2x

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Q: Find the general solution of the Following problem? 9y" + 12y' + 4y = 0

A: Given: 9y"+12y'+4y=0 we know that solution of given differential equation is given by y=aec1x+bxec2x…

Q: Find the general solution of the following: 1. (4D2 – 4D + 1)y = 0 %3|

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Q: Find the general solution: y" + 3y' + 2y = 4e^x

A:

Q: Find general solution of the difference equation Yn+2 + 6yn+1+9yn = n 2" +7, by method of…

A: Given:  The given difference equation yn+2+6yn+1+9yn=n2n+7

Q: Find the complementary solution: (D^3+D)y=x

A: QUESTION- Find the complementary solution:   (D^3+D)y=x

Q: Find the general solution of the following 8. (4D² – 6D + 1)y = 0 %3D -

A:

Q: Find the general solution by substitution or elimination Q6 A: * = x -2 y +t — х —у+2t dt

A: The system is x'y'=1-21-1xy+t2t Obtain the eigenvalues: A-λI=01-λ-21-1-λ=0-1-λ2+2=0λ=±i The solution…

Q: Solve the equation below for y. ons 3x + 2y = 4 %3D O y = -r + 4 O y = -0+2 Ov = +4 O y = -3x + 4

A: The objective is to find the value of y.

Q: Find the general solution of the following 1. (D² – D – 2)y = 0 %3D

A: To find- Find the general solution of the following: D2 - D - 2y = 0

Q: Given that y(1) = 1 and y'(1) = −1, find the solution to x2y'' + 2xy' −2y = 2x2.

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Q: Find the general solution of y" + 9y = 5e^x -162x^2. Use yp Ae^x + Bx^2 + Cx + D.

A:

Q: Find the general solution of the Following problem? 6y" - 5y' - 4y = 0

A: Solution:-  The given differential equation is  6y''-5y'-4y=0................(1)

Q: 1. Solve for x. 3 a. 7 %3D 8. b. %D x+2 5

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Q: Find two different particular solutions for 3a + 4y = 2

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Q: 9. (D2 - 2D +5)²y = 0 %3D

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Q: Find the general solution y" + 3y + 2y = 3e-t cost + 4e

A: To find the general solution of the given differential equation

Q: Q1: Find the solution for these equations: X+2Y+Z=4 .. (1) 3X-4Y-2Z=2. . (2) 5X+3Y-5Z=-1... (3)

A: We have to find the solution X, Y, Z of the given system of linear equations. For this, we have to…

Q: Find the general solution of the following 13. (D² – 2D + 2)y = 0

A:

Q: Find the general solution of the Following problem? 4y" + 4y' + 5y = 0

A: Consider the following differential equation: 4y''+4y'+5y=0 Characteristic equation of the above…

Q: Find a real general solution x^2y"−20y=0

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Q: If y₁(x)=e³x and y₂(x)=xe³* are solutions to y" - 6y' +9y = 0, what is the general solution?

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Q: Q1: Find the solution for these equations: X+2Y+Z=4 (1) 3X-4Y-2Z=2.. . (2) 5X+3Y-5Z=-1 . (3)

A:

Q: Find the general solution for b. у" — 2y" + 4y' — 8у %3D 0

A:

Q: Find the general solution of the Following problem? y" + 2y' + 2y = 0

A: The coefficient of d2ydx2 is 1, the coefficient of dydx is2 and the coefficient of y is 2.

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.