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 \(\mathrm{f}(\mathrm{x})=\)
- A \(\frac{1}{3} \log \left(x^2+y^2\right)\)
- B \((2 x+3 y) \log x\)
- C \(x \log \frac{y}{x}+y^2\)
- D \(\sin \left(x+y^2\right)\)
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 \(y=v x\)…
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