4) In the differential equation of, y(x³ – y)dx – x(x³ + y)dy = 0 - where a and ß are constants, what must a and ß be for µ = xªyB to be an integration factor. Find the general solution of the equation.

Q: For the differential equation (x2 - 4)y" + (x- 2)y' + 2y = 0, a regular singular point is: %3D None…

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

Q: Given that y = e^x is a solution of (x - 1)y" - (x + 1)y' + 2y = 0, find a linearly independent…

A: The solution is given as

Q: 4) In the differential equation of, y(x³ – y)dx – x(x³ + y)dy = 0 where a and ß are constants, what…

A: Question from ordinary differential equations.

Q: 1. Verify that y = (x³ – x) In cx satisfies the differential equation (x³ – x)y' – (3x² – 1)y = x5 –…

A:

Q: Given that y, (x) = x is a solution of the differential equation x2y"- xy' + y = 0. If we use the…

A: Given it is given that y1(x) = x is the solution of the differential equation x2y"-xy'+y =…

Q: For the differential equation (x2 – 16)y" + (x – 4)y' + 2y = 0, the singular %3D points are: O x=4…

A: Let us consider the differential equation y''+P(x) y'+Q(x)y=0 Where P(x) and Q(x) are function of x…

Q: 6. If the function y = a, (1 + 3x + x² + r- :) is a solution of the differential +. equation Ay' –…

A: The solution is given as

Q: For the differential equation (x² – 4)y" + (x – 2)y' + 2y= 0, the singular points are: %3| x=2 and…

A:

Q: 2. The differential equation (4x'y -6xy-2x-3dx + (2x*y – 2.x' kdy = 0 is exact because ƏM ON dy

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Q: 1. Determine whether = is a solution of the differential equation y'--y = 0 3 y' = 6x² а. 6x2-…

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Q: What is the particular solution to the differential equation x(x³ – xy² + 2y³)dy – y(x³ + 2y³)dx = 0…

A:

Q: 1. The standard form of the general first order linear differential equation in y is 2. The linear…

A:

Q: 1-Apply the undetermined coefficients method to find a particular solution of the following…

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Q: 2. The differential equation (4x'y'-6x'y-2r-3)dr +(2x*y-2x' ty = 0 is exact because aN

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Q: Show that y = 3x et +e-3x is a solution of the differential equation y' + 3y = 3ex. 4 y = 2ex + e-3x…

A: Given the differential equation:

Q: For the differential equation (x² – 4)y" + (x – 2)y' + 2y = 0, a regular singular point is: X=4 x=2…

A:

Q: 8. Consider the homogeneous linear equation: 2.a²y" + 3xy' – y = 0, x > 0. (a) Explain why y = e" is…

A: Note: Since these are independent subparts, according to our policy we are only allowed to solve…

Q: Determine the appropriate form for yp on the differential equation y"=9x^2 + 2x -1 a. y=Ax^4…

A: given the differential equation :

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A: Given that a second order differential equation and also given a solution of this equation is xm and…

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A:

Q: 2. Solve the differential equation (3.x² – x³ + 3y – 3.xy – y³)dx + 3(x + y²)dy= 0, - by determining…

A: Exact differential equations solved by using integrating factor

Q: Find the particular solution of the given differential equations. (x² + 2xy - 4y²)dx - (x² - 8xy -…

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Q: x2+1 y'= Ans: y = + x + In(x – 1)² +c = -X - X-1

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Q: Find the particular solution of the given differential equations. 3. (xy + x)dx = (x²y² + x² + y² +…

A: Find the particular solution of the given differential equations.3. (xy + x)dx = (x²y² + x² + y² +…

Q: d³y +3(1- a)z² d´y dy + (3a? – 3a +1)z- - a'y = 0 dz dz

A: We have to find the value of the variable a.

Q: 1. Find a homogeneous linear differential equation with constant coefficients whose general solution…

A: Given:y=C1+C2x+C3e-7x

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A: Given solutions are y1 = x  and  y2 = xln(x)

Q: Find the particular solution of the given differential equations. 2. (x² + 2xy - 4y²)dx - (x² - 8xy…

A: (x² + 2xy - 4y²)dx - (x² - 8xy - 4y²)dy = 0

Q: What is the general solution to the the differential equationy'''=0? A y=C₁+C₁₂x 1 By=C₁+C₁₂x+C₁₂x²…

A:

Q: For the differential equation (x2-4)y" + (x- 2)y' +2y = 0, a regular singular point is:

A:

Q: 3. Consider the differential equation a²y" – x(x + 2)y + (x + 2)y = 0, x > 0 %3D a) Show that yı(x)…

A:

Q: 1. Use the undetermined coefficients method to find the general solution of the given differential…

A: Since this image is asked for multiple answers, as per our answering guidelines we are supposed to…

Q: 6. Find the integrating factor, I of the linear differential equation dy dx A. -x²y B. C. D. e-x²…

A:

Q: 12) Consider the differential equation y" + a1(x)y' + ao(x)y = 9 sin(7x) And suppose that Y1 = x Y2…

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Q: Write down the form of the general solution y = y. + y, of the given differential equation in the…

A: Consider y=emx be the solution of the homogeneous part. The auxiliary equation is m2+w2=0. Simplify…

Q: 2. Find the solution of the differential equation ₂ dy 2x² = dx 3xy + y². which satisfy an initial…

A: Solved below.

Q: 4. If y, (1) = a is a solution of dy dr Find the second linear independent solution and the general…

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Q: 2(a) Show that for any values of the arbitrary constant c, and the function C2 d²y + y = 0 y = c1sin…

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Q: (b). By reversing the role of x and yY or otherwise, find the general solution to the differential…

A: Given:        2x-4y2dydx+y=0            2x-4y2dy+ydx=0    Equation in total differentials:…

Q: 12) Consider the differential equation y" + a1(x)y' + ao(x)y = 9 sin(7x) And suppose that Y1 = x Y2…

A:

Q: 2. Solve the differential equation (3x² – a³ + 3y – 3ry – y*)dx + 3(x + y²)dy = 0, by determining an…

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Q: 2. Find all values of r for which y = e™ is a solution of the second order differential equation y"…

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Q: Find a general solution of the homogeneous differential equation y'= (2xy)/(x^2-y^2)

A: Homogeneous differential equation :   A differential equation of the form dydx=f(x,y)g(x,y) is said…

Q: The General solution of the differential equation 3x2 + 2x + 6 is x3 + x2 + 6x dy using variable…

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Q: Suppose that yi (x) =x² denotes a nontrivial solution of a homogeneous linear second-order…

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