Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y ')²

Q: Find the Differential equation by eliminating the arbitrary constant y= A + bex

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Q: x + 4y3) dy- ydx = 0

A: We have to find the solution of the given non exact differential equation.

Q: The integrating factor of the differential equation as shown is e^(-y).

A: Given that: dxdy+x-y=0

Q: Find the general solution of the first-order linear differential equation. (Use x as your…

A: We can find the correct answer as below

Q: Solve the differential equation using undetermined coefficients method y''+4y=2x sin(x)

A: Given that y''+4y=sin2x Let y=emx Now  m2+4=0m=±2i Therefore the general solution,…

Q: Find the differential equation by eliminating the arbitrary constant y= A + bex

A: Solution:-

Q: What function satisfies the differential equation y - y' = 0?

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Q: Find the differential equation whose solution is given by y = C,et*cos3x + C,e*sin3x

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Q: y + 3xy' – 2(y')³ = 0

A: Product rule of differentiation: (fg)'=fg'+gf' Chain rule of differentiation:…

Q: y=X+ Ci ex t %3D

A: Explanation of the answer is as follows

Q: Form the differential equation for the function 2x-y-Dasin(2x-b)

A: See the attachment

Q: Find general solutions of the differential equation    (x+y)/y'=x-y

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Q: By using substitution of x-e' and t = ln(x), find the general solution of the differential equation.

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Q: Let y' (x) = V1– y²(x) be a differential equation. What is a solution?

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Q: In y = C₁e* + C₂е¯x

A: Given problem:- Find its differential equation through eliminating arbitrary constants.    In(y) =…

Q: Solve the Differential Equation using VARIATION OF PARAMETERS: y''+y'-3y=4sin2x

A: The solution of a differential equation is defined as the function that satisfies the differential…

Q: Find a linear differential equation with constant coefficients satisfied by e2x, e-x, e3x and e6x

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Q: use the method of variation of parameters to find a particular solution of the given differential…

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Q: Find the differential equation by eliminating arbitrary constant  y=Ae-3x+Be2x

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Q: Explain how to solve a separable differential equation of the form g(y) y'(t) = h(t).

A: A separable differential equation is one in which the terms of two variables in the term can be…

Q: Determine the solution to the differential equation given by: y''-2y'+y=sin x

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Q: Find a differential equation whose general solution is y = cie®t + cze¬,

A: The complimentary function of the differential equation if the root of the auxiliary equation are…

Q: The linear Differential equation of any order if there is no constant term s present is known as?

A: We have given The linear Differential equation of any order if there is no constant term s present,…

Q: Find the solution y(t) by recognizing the differential equation

A: Given differential equation - y' = 6300-yWe can write it as - dydt = 6300-ydy300-y = 6dtIntegrating…

Q: Form the differential equation by elimaniting the arbitary constant A,B from y=Ae7x+Be-7x

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Q: Find a differential equation whose general solution is y = cjet + cze-". = 0

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Q: Determine the particular solution of the differential equation yi+yie(x/y}=+2x²e(z/y}? When y(0) = 1

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Q: Form the differential equation by eliminating arbitrary constant  y=Ae-3x+Be2x

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Q: Solve this exact and linear Differential equation in y.

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Q: y"+y = cosecx cotx %3D

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Q: Find the solution of a given non-homogeneous differential equation using the variation of…

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Q: Determine if the function is a solution of the differential equation y''-y=0

A: y''-y=0 y'' represents the second derivative  we find the roots , by writing the given equation in…

Q: Find the general solution of the differential equation: y" – 2y - 3y= - 3te. Fi: of the…

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Q: ylv – y" = 4x + 2xe-*

A: the

Q: How would you solve the differential equation y'=2t-y using separation of variables to find y(1)?

A: Consider the given differential equation, y'=2t-ydydt+y=2t The above equation cannot be solved by…

Q: y² = 14eax-

A: Given y2=14eax

Q: y = 2 -[(1+y(t))sin tdt.

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Q: equation

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Q: . Give an example of a nonlinear differential equation of the formy = f (y).

A: Solution: Nonlinear Differential Equation: A nonlinear differential equation is a differential…

Q: у" - Зу' + 2у %3Dcos(e -*)

A:

Q: Find the solution to the first order differential equation using any acceptable method.…

A: Given: The first order differential equation is (y2+1)dx = (ysec2x)dy.The initial condition is…

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

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Q: (x-C,)' +y° = C;?

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Q: a. y = Ae-3x + Be2* . Derive the differential equation by eliminating the constants

A: here we have to go differentiating and substituting

Q: = Form the differential equation by eliminating arbitrary constants : y = ax +0x , .3

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Q: Solve the given differential equation by separation of variables. аy — е-У +е-4x — у exy dx

A: Solution

Q: Form the differential equation by eliminating constants a and b from y = a(b – x)(b+x) + 56.

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Q: Solve the differential equation using the method of undetermined coefficients. y" - 4y' = sin(3x)

A: Given differential equation is