MHT CET 2017 Math Solved Paper

(b) We have,

dy

dx

=tan(

y

x

)+(

y

x

) ..........(i)
Since, it is homogeneous differential equation After putting, y=Vx, we get

dy

dx

=V+x

dV

dx

V+x

dV

dx

= tan‌V+V [From (i) ]
⇒ x

dV

dx

=tan‌V
⇒

1

tan‌V

dV=

1

x

dx
After integrating on both sides, we get
∫

1

tan‌V

dV=∫

1

x

dx
⇒ ∫cot VdV = logx + logc
⇒ log sin V = log(xc)
⇒ sin v = xc
Hence, sin (

y

x

) = xc