Identify the guess for the particular solution, y, for the following differential equations without finding the actual value of the coefficients. (i) y"-6y'+8y= 2021x+e", given y (x)= qe** +ge". %3D (ii) y"-2y'+ y = (x² + 2021)., given y (x) = qo° +c2xe".

Q: What is the solution to the differential equation 2√√ay- da Oy = ( ² √₂-2) ? 3 Oy=(2²√x - 2) ³ 1 =…

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Q: Consider the following differential equation to be solved by the method of undetermined…

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Q: Solve the Linear Higher Order of differential equation using the formulas below. (xD – 1)(D +x) |…

A: We have to solve the problem

Q: Use the substitution t = x - xo to solve the given differential equation. (x + 6)2y" + (x + 6)y' + y…

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Q: 3. (2xy-x+2y- 1) dx +(4x²y² - x² + 4xy²-x) dy = 0

A: See answer below.

Q: 3. Determine the general solution of the differential equation y/" + 2y" + 2y" + 2y' + y = e¬t + t.

A: Solution of differential equation is solved below

Q: Solve the given differential equation by undetermined coefficients y’’-14y’+49y=42x+5 y(x)=?

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Q: Identify an appropriate method to solve each differential equation. Then solve 3 of the 5 equations.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: What is the value of m in the equation m+) dx + (G+:) dy = 0 to complete the differential equation?…

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Q: ind m so that y =emr is a solution of the differential equation y'=-9y.

A: Take y=emx be the solution, then it must satisfy the given ode.

Q: Q2. Factor out the differential equation and find the general solution.…

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Q: Obtain the particular solution of (3x2-2y2)y'=2xy; when x=0. y=-1

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Q: (x²y3 – e3*)dx + (x³y² + y²e»*)dy = 0 exact %3D |

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Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: dy 2x = (3y + x)- dx

A:

Q: Find the general solution to the differential equation y''-4y'=8-16x

A: Given that the differential equation is y''-4y'=8-16x. It is required to find the general solution…

Q: (4D² - 4D + 1)y= 0; when y(0) = -2; y' = 2; determine the value of y when x = 2

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Q: Find the general solution of the differential equation y" - 36y=-108t + 72t². NOTE: Use t as the…

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Q: 2. (2x– 3y +1)dx - (3x + 2y – 4)dy = 0 |

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Q: Solve the differential equation by variation of parameters. 9x y(x) = y" - 9y = C₁e³r 3x 3x -3.x +…

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Q: Find the solutions of the following differential equations. x2y’ = 1 - x2 + y2 - x2y2

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Q: Use the substitution t = x - xo to solve the given differential equation. (x + 6)2y" + (x + 6)y' + y…

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Q: Find the differential equation of the following function (x + y – 1)dx + (2x + 2y + 1)dy = 0 a. x +…

A: Given differential equation is  (x+y-1)dx+(2x+2y+1)dy=0

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.