II. Solve each of the following DEs by determining its integrating factor. 5. (10xy -8y - 32y-7)dx+ 2(x² + 2xy– 4x)dy = 0

Q: Integrate. √ ( 7x² + 2/17 - 0²³) 0 3x 4+ dx = 0 +C

A:

Q: Evaluate. e13x | de = [ dx (e13x + 7)³ +C

A: The given integral is:

Q: xdy + (3xy + y - e-³x) dx = 0

A:

Q: III. Find the particular solution of each of the following. 3. (y² + x²y + 2x) dx + (x³ + x +…

A:

Q: y′ = 2y − 3

A: Given,

Q: Solve the given equation.. (3x2 + y)dx + (x²y – x)dy =0 Y +3x = C a. b. x²y? + x²y+ x4 = C C. d.…

A:

Q: Find the particular solution of the given D.E. (y²-2xy + 6x) dx + (2xy - x²-2) dy. =0 when X=-2 and…

A:

Q: 2. Solve the ff. equation using integrating factor. dy 2y – e3r dx

A: Given: dydx=2y-e3x

Q: (4xy + 3y²)dx + x(x + 2y)dy = 0 3. %3D

A:

Q: Determine the Solution of the following D.E.: (2) xydx + 2(x2 +2y²)dy D0; when x=0, y= 1

A:

Q: x² + 4y² = C(x+y)

A:

Q: Obtain the general solution of the following equations:    2y(x2-y+x)dx-(x2-2y)dy=0

A:

Q: x² = 2y²(y-1) y² = 2x²(x+1) x² = 2y²(y+1) y² = 2x²(x-1) dx (3x²-2-²) 4

A:

Q: 1. 2(2y²+ 5xy – 2y +4) dx +x(2x + 2y – 1)dy =0 ;y(1) =1 (NEDE)

A: ANSWER: The given differential equation is…

Q: (6x + y?)dx + (2xy – 3y?)dy = 0

A: Image is attached with detailed solution.