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TS EAMCET · Maths · Differential Equations

If the solution of the differential equation \(\frac{d y}{d x}=\frac{2 x+3 y}{3 x-2 y}\) is \(\mathrm{y}=\mathrm{x} \tan (\mathrm{f}(\mathrm{x}))+\mathrm{c}\) then \(\mathrm{f}(\mathrm{x})=\)

  1. A \(\frac{1}{3} \log \left(x^2+y^2\right)\)
  2. B \((2 x+3 y) \log x\)
  3. C \(x \log \frac{y}{x}+y^2\)
  4. D \(\sin \left(x+y^2\right)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{3} \log \left(x^2+y^2\right)\)

Step-by-step Solution

Detailed explanation

\(\frac{d y}{d x}=\frac{2 x+3 y}{3 x-2 y}\) Let \(y=v x\)…