JEE Mains Model Paper 15

dy

dx

=

xy+y2

x2−xy

Put y = vx
∴ v + x

dv

dx

=

v+v2

1−y

∴ x

dv

dx

=

v+v2

1−v

- v
=

v+v2−v+v2

1−v

=

2v2

1−v

∴

1−v

v2

dv = 2

dx

x

(

1

v2

−

1

v

) dv = 2

dx

x

⇒ −

1

v

- log v = 2 log x + const
⇒ −

x

y

- log

y

x

= log x2 + log C
⇒ −

x

y

= log

y

x

= log x2 + log C
⇒ −

x

y

= log (

y

x

.x2C1) - log (C1xy)
∴ C1xy = e−x∕y
xy = Ce−x∕y [ take C1 =

1

C

]