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TS EAMCET · Maths · Differential Equations

The solution of the differential equation \((2 x-3 y+5) d x+(9 y-6 x-7) d y=0\), is

  1. A \(3 x-3 y+8 \log |6 x-9 y-1|=c\)
  2. B \(3 x-9 y+8 \log |6 x-9 y-1|=c\)
  3. C \(3 x-9 y+8 \log |2 x-3 y-1|=c\)
  4. D \(3 x-9 y+4 \log |2 x-3 y-1|=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(3 x-9 y+8 \log |6 x-9 y-1|=c\)

Step-by-step Solution

Detailed explanation

We have, \[ \begin{aligned} & (2 x-3 y+5) d x+(9 y-6 x-7) d y=0 \\ & \frac{d y}{d x}=\frac{2 x-3 y+5}{3(2 x-3 y)+7} \end{aligned} \] Put \(\quad 2 x-3 y=z\) \[ \Rightarrow \quad 2-\frac{3 d y}{d x}=\frac{d z}{d x} \]…