Evaluate the Particular solution of the differential equation and find y when a = 0 and x = 2. If decimals, use 8 decimal places.

Q: Determine whether the given differential equation is exact, if it is exact , solve it. + 1) + y = 3…

A: Exact differential equation

Q: Find the general solution of the differential equation y′ = √x y

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Q: Solve the given differential equation by undetermined coefficients. y" + y' = 8 y(x)

A: The solution to this differential equation can be written as the sum of the complimentary solution…

Q: Solve the differential equation 4x(dxdt)=7, if x=10 when t=0.

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Q: Find a second solution of each differential equation. (1+ x)y" + xy' - y = 0; y1 = x.

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Q: e-(x²+y³)(x dx + y dy) = 0

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Q: y = ce2t + Cze -3t y = ce-t/2 + cze¯ -2t

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Q: Determine if the function is a solution to the given differential equation. et solves y' = 9y + e* 8…

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Q: Determine whether the differential equation (8x² − 2xy + 4) dx + (4y² − x² + 8) dy = 0 is exact. If…

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Q: For each case, find a differential equation whose general solution is:   y = c1e2t + c2e-3t    y…

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Q: In the given question , determine whether the function is a solution of the differential equation…

A: Substitute the value of y in the equation to determine whether the function is a solution to it or…

Q: Determine whether the function is a solution of the differential equation xy' - 4y = x°e*, x > 0. y…

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Q: . Solve for the differential equation and get the particular solution. 1. ye dx (9- e3*)dy; x 0 y= 1

A: Simplify the given equation to separate the variables.     Take integration on both sides of the…

Q: When à = 0 the differential equation becomes X" = 0 which gives the solution X = ax + b.

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Q: Determine whether the differential equation (2x² − 2xy + 3) dx + (2y² − x² + 2) dy = 0 is exact. If…

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Q: (x² + y?)dx – 2x²dy = 0 %3D

A: Given: x2+y2dx-2x2dy=0 So, we can also write as: x2+y2dx=2x2dydydx=x2+y22x2...1 Let, y=vx Now…

Q: equation

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Q: Determine whether the differential equation (5x² - 2xy + 6) dx + (7y² - x² + 5) dy = 0 is exact. If…

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Q: Solve the given differential equation by undetermined coefficients. y"+y+y = x? - 3x y(x) =

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Q: Solve the differential equation y' = x¹y subject to the condition that y = e¹ when x = 0. e4 y(x):…

A: The detailed solution is given below Thank you

Q: Find a differential equation whose general solution is y = c₁est + c₂e-2¹. 5t = 0

A: I have given the answer in the next step. Hope you understand that

Q: Find the differential equation whose general solution is y=c1e4t+c2e-5t

A: Find the differential equation of given solution.

Q: Solve by rewriting the differential equation as an equation for dy , for x21 with y(3) =1 dx dx The…

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Q: Determine whether the differential equation (5.a2 – 2xy + 4) dr + (2y² – x² + 5) dy = 0 - is exact.…

A: The given differential equation is 5x2-2xy+4dx+2y2-x2+5dy=0

Q: 2y²e»* dx + 2xyey° dy = 0

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Q: Find the general solution of the differential equation y′ = x(1 + y)

A: Given differential equation - y' = x1+ydydx = x1+ydy = x1+ydxSeparating variables - dy1+y =…

Q: Solve for the general solution of the differential equation : ( D + 100 ) y = 0

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Q: Determine whether the differential equation (5x + 7) + (5y – 5)y' = is exact. If it is exact, find…

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Q: (D² - 1)y= 2 1+ex

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

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: Use variation of parameters to solve the differential equation x²y" + 10xy' + 8y = x².

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Q: Determine whether the differential equation (7x² − 2xy + 2) dx + (4y² − x² + 7) dy = 0 is exact. If…

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Q: Solve the differential equation xy' = x² + 3y, for x.

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Q: y'+2y = e¯*

A: As per our guidelines we can only solve one question and rest of the question will be reposted.

Q: Find the general solution to the differential equation y = e8*e10y y = help (formulas) Use the…

A: The objective is to find the general solution to the differential equation.

Q: Solve the differential equation 9y' = x + y by making the change of variable u = x + y.

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Q: Find the general solution of the differential equation y' + y = te-t + et and use it to determine…

A: The differential equation is given as

Q: Solve the differential equation by variation of parameters. y" + 2y + y = e-tIn(t) y(t)

A: Given the differential equation is y''+2y'+y = e-t lnt

Q: Find the value of the constant(s) so that the function x (t) = emt is a solution of the Differential…

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Q: Find the general solution to the differential equation y' + 6z°y = a® Use the variable I = CeT" dr…

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Q: Verify that the general solution satisfies the differential equation. Then find the particular…

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Q: Find a differential equation whose general solution is y = c₁e5t + c₂e-²t. = 0

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Q: Use appropriate substitution to solve the differential equation dy 2x + y - 2+ dx 1 4x + 2y > y =…

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Q: 19. (5x2 — у) dx + xdy %3D 0

A: Given (5x2 -y)dx + xdy = 0 (5x2 -y) + xdydx = 0 Calculate whether the differential equation is exact…

Q: x²(y+: x(2y+

A: The differential equation is x2y'=4x2+7xy+2y2. Divide by x2 on both sides, y'=4+7yx+2yx2 Substitute…

Q: Solve the differential equation by variable separable r®y² dæ

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Q: t. t.

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Verify x = e + 2te' satisfies the differential equation [2 x' = 3 x+e

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Q: Determine whether the differential equation is exact. If it is exact, find the solution. (8x² − 2xy…

A: Comparing the given differential equation with the general differential equation Mdx+Ndy=0 we get,…