Question

the differential equation. 1) y - y = ex. y solve the differential equation. 2) (x + y +1) dx - (2x+2y-3) dy = find the general solution, x²-g2 + 2xy) 3) x+1

Couse name is differantial equqtion.Please help.

Answer 1

> > g'-y=et. u2 = y(i+yet) > 2> (x+y+i) dx (2X+27 -3) dy=0 Integroting o dy on both side 5x+7+) dx - 52x+2y-3) dy zo both side dy 14+ y2 et de Integrating Say=5(4+ y2ex) dx *2 + Jx+* - (2xy +242-34)=C 2 11 y = yx + y²e &c y (1-x) + 6² y ² = 6 - y2 + (8 + x) = 2xy ac x² - 27² +64 + 2xy = 4 x 7=26. X²-27² +64- 2xy = 6' X² - 27² + (6-2x) y = c'

3) X+1 x² 4 ² + P(x-4) yt +y'=0 (x-7) [x+y+2) (x+1) e (y+1) d y = 0 exty e ² + (+1) de de et. d. e² ex el. e² + (1+1) dx (T+1) X-Y 2 X-Y exty x.é .e + e ex dy =o x. ex er 2x+P 2x+2 xe dy e ox e [x ex ] dx + y +1) dy +

on both side : Integrating fe' [ xette38) dx + Scy+1) dy = e [skeøkt se det er ty = e² [x * ² 1 2 - 1 1 + 2 + y = 0 ex e Tx e ot + ya 2 ty esexta [ 21-1]+242 + 4y = 6 Ox+2 D (2 4 ² + 4y + (2x+) e y G