Test the exactness and obtain the general solution of the differential equation: 2+ye*y y' =. 2y-xe"y

Q: show that function  y1=x-1 is a special solution of the differential equation y'=1 - ( y-x+1)2 and…

A: Given the differential equation y’ = 1 – ( y – x + 1)2 and we have to show that y  = x -1 is a…

Q: Find the Differential equation by eliminating the arbitrary constant  x2-y2=a2

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

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Q: Find the general solution of the differential equation. (Use C for any needed constant.) y' = 10VX y…

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Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) -…

A: It is given that the differential equation is 2y''+y'-y=x+5 The auxiliary equation is 2r2+r-1=0…

Q: 3. Find the general solution y = Yc + Yp to the differential equation. Use the uppercase letters C…

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Q: 2 (y+ 1) da- ydy = 0

A: Explanation of the answer is as follows

Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''=4

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Q: i. Determine the general solution of the above differential equation.

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Q: Find the general solution of the first order differential equation (x+2) y′ + 4y = (3x + 6)-2 lnx.

A: Given: x+2y'+4y=3x+6-2lnx for finding solution of given differential equation, first we convert it…

Q: Eliminate the arbitrary constants: y= x+ Ce2x + C2e¬x 1.

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Q: Find the value of the arbitrary constant of the particular solution of the differential equation…

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

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Q: Show that the function  y1=x-1 is a special solution of the differential equation y'=1-(y-x+1)2 and…

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Q: Find the general solution of the first order differential equation 2xy(dy/dx)=x2-y2

A: The given differential equation is a homogeneous. See attached file for a step by step explanation.

Q: find the general solution of the first-order linear differential equation. y' + y = ex

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Q: the differential. Equation by eliminating the arbitrary constant  y = Ae2x + Be-2x

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Q: xy"+y'=0; y1=ln(x) How can this second-order differential equation be solved by general solution?

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Q: (D² - 1)y= 2 1+ex

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

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Q: Determine the general solution of the given differential equation

A: Rewrite the equation in standard form. And solve it

Q: What is the particular solution to the differential equation +1+y = 2e- with y = 1, 2=-1 when x = 0?…

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Q: 2. Test the exactness and obtain the general solution of the differential equation: 2+yexy y' =…

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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: Determine the values of r for which the differential equation y'-y = 0, has a solution of the y =…

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Q: y" - y = e2* - sin x

A: The given question has been solved in detail

Q: Eliminate the arbitrary constants in the equation defined by y = ae^(3x) + bxe^(3x). Which of the…

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Q: Find the two power solutions of a given differential equation about the ordinary point x=0. 1.…

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Q: = 2x (y(0) = 4

A: Given: y2y'=2xy(0)=4

Q: Solve the differential equation by variation of parameters, subject to the initial conditions y(0) =…

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Q: y' = xe', У (0) — о

A: We have to isolate the variable then integrate the function to solve the equation

Q: Show that the differential equation dy -2 - yezy dr rezy – 2y is exact and find its solution. 3.

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Q: Use separation of variables to find the general solution of the differential equation. (9 + x)y' =…

A: We have,

Q: Find the general solution of the differential equation using any method          y′ = √( 1 − cos )

A: Find the generla solution of given differential equation y'=1- cos x

Q: The general solution of the differential equation by direct method: dy 57 dz

A: Given- dydx=5x To find- the general solution of the above differential equation. Concept used- In…

Q: Find the value of the arbitrary constant of the particular solution of the differential equation…

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

A: Solution :-

Q: What form of the particular solution is appropriate for the differential equationy'' - y'=4+4e*.

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Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''-2y'=ex

A: Solve for the particular solution of the non-homogeneous differential equation. 1. y''-2y'=ex

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: Solve the differential equation and initial condition and verify that your answer satisfies both the…

A: Given,           y'=2xy2           y0=13

Q: Use the initial condition to find the particular solution of the differential equation. differential…

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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 particular solution of the differential equation satisfying the initial condition…

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Q: For the differential equation y" --y' --= 0, find a particular solution which satisfies the initial…

A: To find the particular solution for the given differential equation which satisfies the initial…

Q: use the method of variation of parameters to determine the general solution of the given…

A: First calculate the complementary function.

Q: A/ By using Exact equation solve the first order differential equation 2y² + ye* + (4xy + x² + 2y)y…

A: Topic:- application of differential equations

Q: Show that the differential equation x¹y³ + x(1+y¹)y' = 0 is not exact, but becomes exact when…

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Q: Use separation of variables to find the general solution of the differential equation. e*(y' + + 3)…

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