TS EAMCET · Maths · Differential Equations
A family of curves has the differential equation \(x y \frac{d y}{d x}=2 y^2-x^2\). Then, the family of curves is
- A \(y^2=c x^2+x^3\)
- B \(y^2=c x^4+x^3\)
- C \(y^2=x+c x^4\)
- D \(y^2=x^2+c x^4\)
Answer & Solution
Correct Answer
(D) \(y^2=x^2+c x^4\)
Step-by-step Solution
Detailed explanation
\(x y \frac{d y}{d x}=2 y^2-x^2\) \(\frac{d y}{d x}=\frac{2 y}{x}-\frac{x}{y}\) \(\frac{d y}{d x}-\frac{2 y}{x}=\frac{-x}{y} \Rightarrow y \frac{d y}{d x} \frac{-2 y^2}{x}=-x\) \(\ldots\) (i) Put, \(\quad v=y^2\) \(\ldots\) (ii)…
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