TS EAMCET · Maths · Differential Equations
The general solution of the differential equation \(2 d x+d y=(6 x y+4 x-3 y) d x\) is
- A \(2 \log |2 x-1|=3 y^2+4 y+\mathrm{c}\)
- B \(\log |3 y+2|=3 x^2-3 x+\mathrm{c}\)
- C \(\log |3 y+2|=x^2-x+c\)
- D \(\log |2 x-1|=3 y^2-4 y+\mathrm{c}\)
Answer & Solution
Correct Answer
(B) \(\log |3 y+2|=3 x^2-3 x+\mathrm{c}\)
Step-by-step Solution
Detailed explanation
\(dy = (6xy + 4x - 3y - 2) dx\) \(dy = (3y(2x - 1) + 2(2x - 1)) dx\) \(\frac{dy}{3y + 2} = (2x - 1) dx\) \(\int \frac{1}{3y + 2} dy = \int (2x - 1) dx\) \(\frac{1}{3} \log |3y + 2| = x^2 - x + C_1\) \(\log |3y + 2| = 3x^2 - 3x + C\)
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