TS EAMCET · Maths · Differential Equations
The solution of \(\frac{d y}{d x}=\left(\frac{x}{y}\right)^{-1 / 3}\) is
- A \(x^{2 / 3}+y^{2 / 3}=c\)
- B \(y^{2 / 3}-x^{2 / 3}=c\)
- C \(x^{1 / 3}+y^{1 / 3}=c\)
- D \(y^{1 / 3}-x^{1 / 3}=c\)
Answer & Solution
Correct Answer
(B) \(y^{2 / 3}-x^{2 / 3}=c\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{gathered} \frac{d y}{d x}=\left(\frac{x}{y}\right)^{-1 / 3} \\ \Rightarrow \quad y^{-1 / 3} d y=x^{-1 / 3} d x \end{gathered} \] On integrating both sides, we get…
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