
dy/dx = y-x/x-y ydx + 2(x+y) =0 y' + 2xy = x^3 (x+y)dx + xdy =0
2) a) Let w = xdy - ydx and j:M - RP the inclusion of a bounded region with regular boundary am. Show that the area of M is given by (1/2) Som j*w. b) Let w= xdy dz - ydx dz + zdx A dy and j:M CRP the inclusion of a bounded region with regular boundary am. Show that the volume of M is given by (1/3) Som j*w.
Thank you!
xdy - ydx ф 30v2 where c is the boundary of the 3 Evaluate the line integral 1 segment formed by the arc of the circle x2 +y2-4 and the chord y-2-1 for x 2 0.
xdy - ydx ф 30v2 where c is the boundary of the 3 Evaluate the line integral 1 segment formed by the arc of the circle x2 +y2-4 and the chord y-2-1 for x 2 0.
7- Evaluate each of the following line integrals: (a) /xdy-ydx, c(t)-(cost,sint), 0<t<2π (b) xdx+ydy, c(t)-(cos(), sin,OSIS2 (c) yzdx +xzdy +xydz, where c consists of straight-line segments joining (1,0,0) to (0,1,0) to(0,0,1)
7- Evaluate each of the following line integrals: (a) /xdy-ydx, c(t)-(cost,sint), 0
Find the general solution to the differential equation
dx sin χ xdy +3(y +x*) = sinx
dx sin χ xdy +3(y +x*) = sinx
The solution of the Initial-Value Problem (IVP) (x + y)dx - xdy = 0 ((1) = 0 is given by y = fer-1 - 1 0 None of them Oy= x ln(x + y) y=x Inc Oy= (x + y) Inc
36. The quarter-disk Izl < 1, x > 0, y > 0 onto the exterior of the unit circle |w| = 1.
36. The quarter-disk Izl 0, y > 0 onto the exterior of the unit circle |w| = 1.
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2 marks] tured closed disk B.(0 )"-{ (z, y) E R2 10c x2 + y2 < 1}
(i) Give an example of a function f(x,y) that is defined and continuous on the closed unit disk B(0) ((,y) E R2 but does not achieve a maximum on the punc- 2...
Solve the differential equation. 4xdy + ydx = 24x'dx 0. с y=
The differential equation (x - y)dx + xdy=0 is a Homogeneous differential equation. Select one: O True O False Which of the following linear differential equations is obtained after applying a suitable substitution to the Bernoulli equation (cos 2)y' + 5(sin x)y = cos 1 Select one: 5 tan O A. Vt 3 10 tan OB. + 3 10 tan : Ocot 3 5 tanz OD. + 2 COS 3 casa 3 2 Cosz 3 U COST 2 5 tan...