Question

c. exact with solution ZXY+y+C d. exact with solution 2xy +y=c e. not exact lemy 8. The solution of (x +2y )dx + ydy = 0 is a. Inx+ln(y+x)=C b. 1((v+x)/x)=C c. 1(y+x)+x/(x+x)=C d. In(y+x)+x/(y+x) +c e. it cannot be solved

Answer 1

solution (x424) dx + y dy=0 Solution- o This is homogenous e Differential Equation. putting y=xt Differentiate with respect to 'x' Therefore 22 df +. - (2+2x+) xt a dt tt + (1+2+) + ²+2t + 1 =0 da + - + + ca o t at & dx = 0 Variable seperable (t+1)2 on intergration - 1 (t+1)dt (t+1)2 (t+1

in * set +14=! log (tts) + 1) + log(x) = c' log( 264+4)] + the c! [okake lon - 1+ X - option Ç