For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show all work.

Q: solve y''-y'=xex using variation of parameter . Do not use any formula

A: using variation of parameter . First we find the solution for homogeneous equation. From that…

Q: An Object moved in horizontal coordinate line according to f(x) = x^3 - 6x^2 , where f is directed…

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Q: Find the first and second derivates of the functions. h(t) = t^4 - 7t^3 + 5t^2 - 8t - 14…

A: Find the first and second derivative of the function

Q: y' - y/x = xy2

A: Use the definition of Bernoulli differential equations.

Q: Differentiate the function. y = V7 + 4e3x y' = %3D

A: The function is  y=7+4e3x

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A: We need to evaluate the derivative of the following function y = x3log3x

Q: f(x,y)=x^4+y^4-4xy Find all the endpoints of the function.

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Q: Find y' for the function. (y-4)²-3x² y br |5

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Q: Find fif f'(x) 12x3 + 6x + 7 and f(1) = 2. Answer: f(x)=

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Q: Evaluate Solve y'' - 2y' + y = e^2x by using variation parameters

A: Idea: solving by using method of variation of parameters

Q: Determine y' if y =  x9 − 5x4 + 15x x4 .

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Q: 7. Given the function 8(x)%3D4X' - 3x² +x-1, find g(0), g(-1), and g(x-x) |

A: Some important formulas (a - b)3 = a3 - 3a2b + 3ab2 - b3 (a - b)2 = a2 - 2ab + b2

Q: A particle is moving in such a way that its displacement xcm from the origin after t seconds is…

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Q: For the function ​f(x)=2e^−x^3​, find f′′(x). Then find f′′​(0​) and f′′​(1​).

A: To find f''(x)

Q: For the equation, 2y(x^2 - y + x)dx + (x^2 - 2y)dy = 0, what is the solution

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Q: Find p′(t), p′′(t), and p′′′(t) for the function p(t) = t^(100)+ 4e^(t)+ 16. (You can use rules or…

A: The function is p(t)=t100+4et+16