Except for degenerate cases, the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 defines a(n) _______ if B2 - 4AC = 0.

Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex² False True O

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Q: The particular solution of y+y-2y = e?x is

A: To find The particular solution of the given D.E.

Q: Find the general solution of (D²-7DD' + 12D'2)Z = sin(x - 2y) + ex-2y

A: This question is from linear partial differential equation.

Q: Solve the given Bernoulli DE: 3y' + 3y/x = 2x4y4

A: A detailed solution is given below

Q: 1) Eliminate the arbitrary constants A and B from the equation y = Ae2x + Bxe²x

A: Given equation is: y=Ae2x+Bxe2x                                                    (1) Since, given…

Q: Determine the General Solution of ye2x dx = ( 4+e2x %3D ) dy

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Q: Find the General Solution of (D² + 5DD' +6D2)Z = 10 cos(x - y)

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Q: Find the general solution of 3(3x2 + y2 )dx – 2xydy = 0.

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Q: 4) Find the solution of y'= 2(2xy) passing through (0,1).

A: Given, Equation  y'=2(2x-y) passing through a point (0,1).

Q: Find the general solution of y" – 3y' + 2y 1+e-x°

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Q: Part III Obtain the particular solutions of the following: c. y°dx + (x* +3xy + 4y* )dy = 0, y(2)=1

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Q: Give the general solution of xy²dy = (x³ + y³)dx in explicit form.

A: Given differential equation is  which is homogeneous differential equation.

Q: eУ + 2ху'- у %3D0

A: Given equation is, ey'+2xy'-y=0y=ey'+2xy'...1 Multiplying by y in equation (1), we get…

Q: 1. 3(3x² + y²)dx – 2xydy = 0 -

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Q: Solve the Cauchy euler equation 3x2+ 6x-6y = 3 + Inx d²y + 6x2-6y = 3 + lnx³ dx3

A: In the given question we have to solve the given Cauchy Euler equation. Method: the Cauchy Euler…

Q: solve the solution of the Bernoulli's equation 3yły' + - 8(x + 1) = 0; y(0) = 0 x+1

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Q: Solve the initial-value problem. x²y' + 2xy = In(x), y(1) = 5 %3D

A: givenx2y,+2xy=ln(x), y(1)=5y,+2xy=ln(x)x2this is a standard form of linear diffrenetial…

Q: Which of these gives a general solution to d [ 2 dt 3 2

A: In the given problem we have to solve the given differential equation. Concept: consider a system of…

Q: 3. Find the general solutions of, x+y dx x-y, a.

A: We have to solve the given differential equation.

Q: Find the General Solution of (D² + 5DD' + 6D²)Z = 10 cos(x – y)

A: Given partial differential equation is D2+5DD'+6D'2Z=10cosx−y. We have to find the general solution…

Q: Solve the initial-value problem (3x +9xy + 5y²)dx-(6x² +4xy)dy = 0 y(2) = -6 %3D

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Q: what is the general solution of d^3x/dt^3 - 19 dx/dt + 30=0

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Q: Solve the below equations by Gaussian elimination metho- x +z = 1, 2x +y+z 0, x+y+ 2z = 1

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Q: The equation y3 = 3Bx is the general solution of 3y Oy Oy 3xy Ou' = 3y

A: We will form the differential equation using given solution

Q: Find the general solution of xy²dx = e

A: By using variable and separation method

Q: 2 Find the solution. ху'+ ху %3D 1-у, у(1) %3D 0 A y = x-'(1 – el-') B x = y-'(1 + el-) В © 2y =…

A: Solution of the differential equation

Q: The solution of the DE (4xy + 3)y' =-2y² +1 is O None of these 2xy2 + x + 3y = c 2xy -x+ 3y = c…

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Q: Which of these gives a general solution to d -1 dt 2 -1

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Q: Show that y = x (1 – e*-1) is a solution | to y" – y' + e"-1 = -1

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Q: Solve the Cauchy euler equation d²y + 6x 2-6y = 3 + Inx3 dx x3 d3y 3x2 dx2 dy dx3

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Q: dy + ydx %3D = 3x²y?dx,

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Q: Find the solution of (1 + e²)yy = eª that passes through (0, 1).

A: (1+ex)yy'=ex(1+ex)ydydx=exseparation of variablesydy=ex1+exdxIntegrating both…

Q: Find the general solution of the given DE 2xy^2 + 4 = 2(3-x^2y)y'

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Q: d²y 4y 3e2x. %3D dx2 3.

A:

Q: 6. Determine the General Solution of this Equation in terms of C y2-x+e2x =DC y+x-e2x C. None of the…

A: To find the general solution of the differential equation in terms of C :            dydx+1xy=xy2

Q: - EXAMPLE 3 Find the particular solution of 3xy' y = lnx + 1, satisfying y(1) = -2. x > 0,

A: It is a first order differential equation.

Q: Show whether the two equations y₁ = using the Wronskian. 12e and y2 1.2e are independent or…

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Q: 5. Find the particular solution of x²y' – 2xy = x* + 3; where y = 2 and x = 1

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Solve the following using Gaussian elimination: 3x + 5y + 3z=1 4x + 7y + 6z=4 6x + 7y + 4z=2

A: system Ax=b is 353476674xyz=142 augmented matrix is  353147646742 R1← R1·13 =15311347646742 R2←…

Q: Then the general solution of this DE is :

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Q: dy dx + 3x²y = 6x²

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Q: Determine the General Solution of ye2x dx = ( 4+e2x ) dy %3D

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Q: 11. Solve the following using Gaussian elimination: a) 3x +5y=8 2x + 3y=7 b) 2x + 3y + z=1 3x – y -…

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Q: Find the general solution of the DE y" + 4y + 4y = e²x

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Q: Solve the Cauchy euler equation dy 3x2 d²y + 6x -6y 3+ Inx3 dy dx3 dx2 dx

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Q: 5. Find the particular solution of x²y' – 2xy = x* + 3; where y 2 and x = 1

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Q: Solve the Bernoulli equations x2y' + 2xy = y3

A: First, divide the whole equation x2y'+2xy=y3 by x2y3 to convert it into the form of…