The solution of the differential equation `2x(dy)/(dx)-y=3` represents `c i r c l e s` b. `s t r a igh t\ l in e s` c. `e l l i p s e s` d. `p a r a bol a s`

Explanation

Correct answer is D



`2 x frac{d y}{d x}=y+3 Rightarrow frac{d y}{d x}=frac{y+3}{2 x} Rightarrow frac{2 frac{d y}{d x}}{y+3}=frac{1}{x}`



By Integrating each sides



`int frac{2 frac{d y}{d x}}{y+3}=int frac{1}{x} `

`
Rightarrow 2 log (y+3)=log x+c `

`
...