Classify the following DE's as Exact, Non-exact, Homogeneous or Bernoulli. C:(y² + yx)dx – x²dy = 0 dy A: (-xysinx + 2ycosx)dx +2xcosxdy= 0, B: (3x?y+ e)dx + (x³ + xe – 2y)dy = 0, D: =y(xy4 – 1) dx A is Exact, B is Homogenous, C is Bernoulli, D is Non – Exact. b. A is Non - Exact, B is Exact, C is Homogenous, D is Bernoulli A is Non - Exact, B is Exact, C is Bernoulli, D is Homogenous. d. A is Exact, B is Non - Exact, C is Homogenous, D is Bernoulli. a. C.

Q: Divide by g (y) to separate the variables: dy IP fi O dy || gt h = 7/²010 y de 9х = прто

A: ∫xndx=xn+1n+1+cgiven  dydx=x6ypasses through  (1,3)

Q: Evaluate cex-y) dx + C (x+3Y) dy C:xaxis from (0,0) to (0,-3) and 0-3) to (5,-3).

A: To Evaluate: ∫C2x-ydx+x+3ydyC: x-axis from 0,0 to 0,-3 and 0,-3 to 5,-3.

Q: Evaluate the value of I = (4,0). I = Sleby. r 3x) dx + (6xe6y + y)dy, where I is the straight line…

A:

Q: 1. Evaluate ſ. (x² – y²)dx + x dy along c: x = t³, y = t 1st<8

A: Given:    x=t23 , y =t  (1≤t≤8)    =  ∫cx2-y2dx+xdy     =∫18t43-t223t-13dt+t23dt…

Q: 2. f(x,y)= 2x + 6xy +y

A: Partial derivative

Q: Find dy du du dx dy when y and u are defined as follows. dx u = 3x - 9x² and y = √u

A:

Q: Find (y - 1)(3y² - 2y + 1) [(y - 1) (34² dy. +1

A: We are required to find: ∫(y-1)(3y2-2y+1)y2+1dy

Q: b) Evaluate the value of I = S(eºy − 3x) dx + (6xey + y)dy, where C' is the parabola y = C (0, 0) to…

A: The integrand is given here as         (e6y - 3x)dx + (6xe6y + y)dy        = (e6ydx + 6xe6ydy) -…

Q: If w = 9x² - 4y, x = -6s+3t, and y = = Provide your answer below: Əw = Ət -4s + 9t, find dw Ət in…

A: Please see the below picture for detailed solution.