(MULTIPLE CHOICE) Which of the following equations is(are) variable separable? dN + N = dt N dr (A) y In r dy リ+1 (C) tel+2 2y +3 dy (B) da dy (D) dx ry + 2y – x – 2 %3D %3D 4x +5 xy – 3y – x – 3

Q: Evaluate (2x - y) dx + (x + 9y) dy. C: x-axis from (0, 0) to (0, -9) and (0, -9) to (4, -9)

A: Solution :-

Q: d³y d'y +5dy ² + y = +3. dt3 dt² dt d³x d²x dx +4 +6 +8x dt³ dt² dt

A:

Q: Step 4 Finally, determine(-3x + 7) and (x + 7) and simplify the result. dx dx 1. du 1 dv + U dx V dx…

A: formulas we use: ddxf+g=dfdx+dgdxddxkx=k; k is a constant.dkdx=0; k is constant.ddx(x)=1.

Q: (6x + y2) dx + y(2x - 3y) dy = 0. evaluate

A: The given differential equation is                                    (6x+y2)dx+y(2x-3y)=0

Q: (4х — 5у + 6)dx + (7x— 2у — 3) dy %3D0

A: Given that 4x-5y+6dx=7x-2y-3dy=0dydx=-4x-5y+67x-2y-3this form is equation reduciable to homogeneous…

Q: dx 1. dy y 3x :-5x2 dy 2y 2. dx = -4x²

A:

Q: Solve y (1 + 2 x y) dx + x (1 – 2 x y)dy = 0 using the substitution Z = 2 x y

A: Given that y (1 + 2 x y) dx + x (1 – 2 x y)dy = 0  Therefore, we have  y (1 + 2 x y) dx + x (1 – 2 x…

Q: x^2+3y^2+4y=19; dx/dt=7 when x=2 and y=-3; find dy/dt dy/dt= simplify the answer…

A:

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) 21

A:

Q: d Find dx 0.4 - 2 - 3.7x + 8x d 0.4 - 3.7x - 2 + 8x = dx

A: SOLUTION-

Q: ( 2x + 3y)dx + (3x – 2y)dy = 0 O x² – 3xy – y² = C 2. h O x² + 3xy – y² = C 2. x²- 3xy + y =C x² +…

A: Exact differential equation

Q: Suppose x andy are variables satisfy the equation x2 - y = 12. What is 3x3 dy A %3D dx 2y dy 3x4 dx…

A:

Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: Solve (yz + хуz) dx + (zx + хуz) dy + (ху + хуz) dz =

A:

Q: dy + (ax – 7)y = bx° dx %3D - a = 2 andb = 1 dy + (2x - 7)y dx = x² 6.

A:

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 323 2

A: Here to find the value of line integral we consider two path c1 :from the point (0, 0) to (0, -7)…

Q: d³x d2x dx -2- =0 dt dr3 dr?

A:

Q: (x – 2) dx +4(x+y- 1) d

A: Given       (x-2)dx+4(x+y-1)dy=0

Q: Evaluate. 1 -2 (6x +y) dx dy 0 -5 1 -2 | (6x + y) dx dy =(Simplify your answer.) %3D 0-5

A:

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Given that 7x+3ydx+3x-8y3dy=0

Q: dw Find ду dw at the point (w, x, y, z) = (3, - 1, - 1, - 1) if w = x3y? + yz-z° and x2 + y? +z? =…

A:

Q: Identify whether the following equations are linear or non-linear dy a. +y = 0 dt dx b. + x2 = 0 dt…

A:

Q: (xy2 +2xy -8y² – 16y)dx + (x2 - x - 6)dy = 0; when x = 1, y = 1 %3D %3D a.

A: Given differential equation is   (xy2+2xy-8y2-16y)dx+(x2-x-6)dy=0 ; when x=1 ,y=1

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

A: