Q90 / 170 · Manipal (MET) 2017 · Mathematics

The solution of the equation $(2 y-1) d x-(2 x+3) d y=0$ is

  • A
    $\frac{2 x-1}{2 y+3}=c$
  • Correct answer
    B
    $\frac{2 x+3}{2 y-1}=c$
  • C
    $\frac{2 x-1}{2 y-1}=c$
  • D
    $\frac{2 y+1}{2 x-3}=c$

Solution

The given equation is $(2 y-1) d x-(2 x+3) d y=0$ or it can be rewritten as $\frac{d x}{(2 x+3)}-\frac{d y}{(2 y-1)}=0$ On integrating both sides, we get $\begin{gathered} \int \frac{1}{(2 x+3)} d x-\int \frac{1}{(2 y-1)} d y=0 \\ \Rightarrow \frac{1}{2} \log (2 x+3)-\frac{1}{2} \log (2 y-1)=\frac{1}{2} \log c \\ \Rightarrow \log \left(\frac{2 x+3}{2 y-1}\right)=\log c \Rightarrow \frac{2 x+3}{2 y-1}=c \end{gathered}$

Hence, the correct answer is option: 'B'.

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