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TS EAMCET · Maths · Differential Equations

The general solution of the differential equation \((x-2 y+1) d y-(3 x-6 y+2) d x=0\) is

  1. A \(\left|x+2 y+\frac{3}{5}\right|^{2 / 25} \cdot e^{115(x+2 y)}=C\)
  2. B \(\left|x-2 y+\frac{3}{5}\right|^{2 / 25} \cdot e^{1 / 5(x-2 y)}=C\)
  3. C \(\left|x-2 y+\frac{3}{5}\right|^{2 / 25} \cdot e^{1 / 5(6 x-2 y)}=C\)
  4. D \(\left|x-2 y+\frac{1}{5}\right|^{2 / 25} \cdot e^{1 / 5(x-2 y)}=C\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left|x-2 y+\frac{3}{5}\right|^{2 / 25} \cdot e^{1 / 5(6 x-2 y)}=C\)

Step-by-step Solution

Detailed explanation

Given differential equation \((x-2 y+1) d y-(3 x-6 y+2) d x=0\) \(\Rightarrow \quad \frac{d y}{d x}=\frac{3(x-2 y)+2}{(x-2 y)+1}\) Put \(x-2 y+1=t \Rightarrow 1-2 \frac{d y}{d x}=\frac{d t}{d x}\)…