(3x-y+6)dx + (6x -2y-6) dy=0 hint: Case 1

Q: Find the differential equation whose solutions correspond to the following equation 1. y = C1e¬* +…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: ye2xdx = (4 + e2x)dy %3D

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Q: Find the general solution of the differential equation using any method            dy / dx = √(4 −…

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Q: The general solution of the differential equation x²y" - 2y = Inx is

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Q: For the differential equation x-4y"-2y'+y 0, the point x = -2 is Select the correct answer.

A: One distinguishes the following cases: Point a is an ordinary point when functions p1(x) and p0(x)…

Q: Solve the differential equation listed below:

A: Separate the variables

Q: Solve the given differential equation by separation of variables. dP = p - p² dt P ||

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Q: 2) y"-y'-2y=sin2x

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

A: Given that Find a particular solution to the differential equation using the Method of Undetermined…

Q: y(4) + 2y" + y = (x – 1)?

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Q: Find general solution to the differential equation A-2xy'= 3y

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Q: Find the general solution of each of the differential equations. y" + 9y = 0

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Q: Find the general solution (or the initial value solution if applicable) of the following ordinary…

A: We will find out the general solution for given differential equation using power series method.

Q: The solution of the differential equation dy dx 6. is 6x + C 6lnx + C | 4 6x + C 5 6lnx + C 2

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Q: b. 6y²dx – x(2x³ + y)dy = 0 -

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

A: We have given y=3e2x-4sin2x Then,…

Q: Solve the given differential equation by separation of variables. dy - xy + 3x - y - 3 dx xy - 4x +…

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Q: Solve the given differential equation by separation of variables. xy + 5x - y -5 xy - 2x + 6y - 12…

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Q: Find the general and Singular Solution of the Following differential equation y-2px + yp²=0

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Q: dy 2x dx = 3xy + y? ;y(1) =-2

A: dydx = 3xy+y22x2

Q: 2ху+3у? dy 7. dx x2+2xy

A: Solution of these differential equation  Using y= vx

Q: 2. (1-y) y' = x2

A: The given DE is: (1-y)y'=x2...(1)

Q: A particular solution of the differential equation y''+3y'+2y=4x+3 is:

A: Solving the differential equation

Q: Solve the given differential equation by separation of variables. dy xy + 5x - y - 5 dx xy - 2x + 6y…

A: We can solve the given differential equation by using the variable separable method.

Q: Find general solutions of the differential equation    2xy+x^2y'=y^2

A: Given

Q: Find general solutions of the differential equation       3y+x^4y'=2xy.

A: This can be solved using the standard format: dy/dx + P(x)y = Q(x)

Q: Given the differential equation 2 +5 , find the particular solution, y = f(x), 3y with the initial…

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: Find general solutions of bernoulli differential equations.   xdy + ydx = x^3 y^6 dx

A: For linear differential equation ,dydx+P(x) y = Q(x)Soultion is :y x I = ∫IQ(x) +Cwhere I = e∫P(x)dx

Q: find the solution of this differential equation (x + 2y − 1)dx + (2x + 4y − 3)dy = 0

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Q: 1.3x – xy = c -

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Q: Solve the given differential equation by undetermined coefficients. y" + 2y = 2x + 3-e-2x y(x) =

A: Follow the procedure given below.

Q: find the general solution of the given differential equation. 5.y″ + 2y′ = 3 + 4 sin(2t)

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Q: dy dx 6e²x-y

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Q: Solve the given differential equation by undermiNed coeFFicients. 1. y" +6y +9y = -xe 4x

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Q: Find general solutions of the differential equation      2x^2y+x^3y'=1

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Q: Solve the given differential equation by undetermined coefficients. y"' – 3y" + 3y' - y = x - 3e*…

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: Given the differential equation y" – 2xy' + 5y = 0. Determine the first three nonzero terms in each…

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Q: Solve the given 2. (4) - 2y + y = et +1 differential equation by undermiNed coeFFicients.

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Q: find the solution of this differential equation: xdy − ydx − xy^3 dx − xy^3 lnxdx = 0

A: Given differential equation: xdy−ydx−xy3dx−xy3logx dx=0 y'=yx+(1+log(x))y3

Q: Solve the given differential equation by separation of variables. dy xy + 6y-x-6 = dx xy-7y+x-7

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Q: Find general solutions of the differential equation    y'+3y =3x^2e^-3x

A: y'+3y=3x2e-3x Comparing with y'+Py=Q, we get P=3  &  Q=3x2e-3x Now integrating factor is,…

Q: 2. A solution for the differential equation is y = Pe-3x/2+ Qe¬x!2.

A: Let's find.

Q: The complete solution to the nonhomogeneous differential equation, (D^2 +D - 6)y = 2x, is *

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Q: Solve the differential equation as follows: 8x(x² + 3xy + y-1)dx + (28x³ + 5x*y¬'+ 6x²y=² + 6y¯z)dy…

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Q: 2. Solve the given differential equation by undetermined coefficients. y" + 2y = 2x + 9 – e-2x

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Q: (2x+ykdx– 3(2x+ y+4)dy=0 1.

A: Note: We are required to answer only the first question, unless specified.