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: A Ferris wheel is 20 meters in diameter and boarded from a platform that is 1 meter above the…

A: Given: A Ferris wheel is 20 meters in diameter and boarded from a platform that is 1 meter above…

Q: The differential equation has as a solution. Applying reduction order we set y = uxª. x² d²y dy dx²…

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

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

A: See answer below.

Q: be sec of SIze an B SiZe HOW mons funce ions f:A B are there chas for every beB, there eleme n Es…

A: Given that the size of set A is  8 and size of set B is 4. Now to be total number of functions f:A→B…

Q: а. (4x3 — 6ху^)dx + (4y- 6ху)dy %3D 0 b. 1 -(xdy- ydx)=0 x²+y? с. 1 (v²dx+x²dy)=0 (x2-у?) d. (x+y)dx…

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Q: Q1) Solve the following differential equations: 3. (x- 1)+ 2(x- 1)-4(x-1) + 4y = (1-x)?

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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: 1) y = c x2 2) y = ce* + c2e¬*

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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: Consider the differential equation: y''+12y'+36y=-2x2-4e-3x. Apply the method of undetermined…

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

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Q: Find the differential equation of the following function (3х + 2у + 7)dx + (2x — у)dy %3D 0 а. Зx? +…

A: Exact differential equation

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

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

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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: 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

Q: y' = 4x(2y-³-y)

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Q: (a) y' — 5y = −5ty³ (b) x + 5y = 2x²yª, y(1) = 3 dr

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Q: 3. Solve following differential equations by variation of parameters. (1) y" - 3y + 2y = xe³x (2)…

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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.