Question

Solve: 2xy-y=2 and 2y-4x=2​

Answer 1

Step-by-step explanation:

dy

=

2y−4x+1

2x−y+2

Substituting v=2y−4x⇒

dx

dv

=2

dx

dy

−4

2

1

(

dx

dv

+4)=

v+1

2x+

2

1

(−4x−v)+2

=−

2(v+1)

v−4

⇒

dx

dv

=−

v+1

5v

⇒

v

dx

dv

(v+1)

=−5

Integrating both sides w.r.t x, we get

∫

v

dx

dv

(v+1)

=∫−5dx

⇒logv+v=−5x+c

⇒log∣2y−4x∣+2y−4x=−5x+c

⇒log∣y−2x∣+2y+x+log2=c

x+2y+log∣2x−y∣=c