Obtain the implicit form of the differential equation of the following relation: y -3=x³(3e* +c)

Q: 5x y = C, + C2e4x 4

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

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Q: y = C, cos 3x - C sin(-3x)

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Q: y + 3xy' – 2(y')³ = 0

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

Q: Find the differential equation of the cubics : cy^2= x^2 ( x - a ) with a held fixed.

A: Here c is arbitrary constant and a  is fixed. So we have to find a differential equation which does…

Q: y = Ce * + C2e 2x + C3e * + e 2x

A: y=c1e-x+c2e-2x+c3e-x+e2xy=c1+c3e-x+c2e-2x+e2x Here, complimentary solution is  y=c1+c3e-x+c2e-2x…

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

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Q: Solve for the non-homogenous linear differential equation: y''+4y=cos^2(x)

A: Given; y''+4y=cos^2(x)

Q: The indicial equation for the differential equation 2xy" + y + xy = 0 is 2c² - 1 = 0. True False

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Q: What is the solution to the differential equation 2 = 2xy satisfying the boundry condition y = e…

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Q: What is the differential equation obtained by eliminating the parameter A from the relation…

A: The explanation of answer as follows

Q: The differential equation formed by eliminating arbitrary constants a and 6: y = ax + bx+9 is

A: Given that

Q: b Show that y = e' sinx %3D satisfies the differential equation (1 - x²)y" – xy' - y = 0. |

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Q: What is the standard form of this linear differential equation in one variable. Y + 1)dx + (4x – y)…

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Q: Determine the solution to the differential equation given by: y'=6y2/x

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Q: Find the differential equation that has y = C1 + C2x as its general solution.

A: To find the original differential equation we  have to eleminate the arbitrary constants by…

Q: 4. Solve this linear differential equation by using the appropriate integrating factor +y =x - 1+

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: Find the differential equation whose general solution is y = C1x + C2ex. %3D

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Q: Obtain the differential equation associated with the primitive y = Ae3x + Be2x + Ce*.

A: Given differential equation is we have to obtain the differential equation associated with the…

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

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Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

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

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Q: Find the solution to the differential equation dx 8xy which passes through the point (0,e). Express…

A: We will solve the equation by method od separation of variables.

Q: Find the solution for the second order differential equation y-4y = x sinh x.

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Q: 4.y = C₁e-2x + C₂e³x

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Q: form the differential equation corresponding to (y – b) = 4(x -a) %3D

A: Given: The equation is (y-b)2=4(x-a)   To determine: The differential equation from the equation…

Q: Form the differential equation for the function x+2y=a sin3x-bcos3x

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Q: Find the solution to the differential equation   that passes through the origin.   z=

A: As the solution function to the given differential equation, passes through the origin we will have:…

Q: 2.Form the differential equation from the family of curves y² = Ae³* + Be* , where A and B are…

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

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Q: Find the differential equation by eliminating the arbitrary constant/s. 1. ecosx = c(1-cosy)-¹

A: Since you have asked multiple questions in a single request we would be answering only the first…

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

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Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: If the particular solution is: y=2excos3x                                        ....(1) The first…

Q: Give the general solution of the differential equation y'-y = sinx + cos2x +e-x

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Q: Find every nonzero solution of the differential equation y = y +2y°.

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Q: Give the detailed solution of this differential equation using 1st order and 2nd order 1. (y') ² +…

A: This is a problem of differential equation.

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

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Q: (メyーx+24 -2) dx- (x+ 4x) 0

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Q: Solve the given differential equation by separation of variables. y In(x) *- (1)* %3D Ap

A: Solution :-

Q: (4) Form the differential equation by eliminating the arbitrary constants a and b from y ae" + be-ª.

A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

Q: y = C1e2" sen(x)+ C2e²" cos(x) +x² + C3x + C4.

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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: (D² + 4) y = tan 2x

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Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: Given: The differential equation y'tanx=a+y with initial condition yπ3=a for 0<x<π2. To find:…