TS EAMCET · Maths · Differential Equations
If the solution for the differential equation \(y^2 d x+\left(x^2-x y-y^2\right)\) \(d y=0\) at \((2,1)\) is \(x+y=k\left(x y^2-y^3\right)\), then \(\mathrm{k}=\)
- A \(-3\)
- B \(-4\)
- C 4
- D 3
Answer & Solution
Correct Answer
(D) 3
Step-by-step Solution
Detailed explanation
\(y^2 d x+\left(x^2-x y-y^2\right) d y=0\) \(\Rightarrow \frac{d y}{d x}=\frac{-y^2}{x^2-x y-y^2}=\frac{-\left(\frac{y}{x}\right)^2}{1-\left(\frac{y}{x}\right)-\left(\frac{y}{x}\right)^2}\) Let \(y=v x \Rightarrow \frac{d y}{d x}=v+x \frac{d v}{d x}\)…
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