JEE Mains Model Paper 13

(xy3−x2)dy - (xy + y4) dx = 0
⇒ y3 (x dy - y dx) - x (x dy + y dx) = 0
⇒ x2y3 (

xdy−ydx

x2

) - x d (xy) = 0
⇒ x2y3 d(

y

x

) - x d (xy) = 0
⇒ (

y

x

) d (

y

x

) -

d(xy)

x2y2

= 0
⇒ Integrating

1

2

(

y

x

)2 +

1

xy

= C
It passes through (4, -2) ⇒ C = 0
∴ y3 = - 2x