WBJEE · Maths · Differential Equations
The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is
- A \(y^{2}+x y^{\prime 2}-y y^{\prime}=0\)
- B \(x y y^{\prime \prime}+x y^{\prime 2}-y y^{\prime}=0\)
- C \(y y^{\prime \prime}+x y^{\prime 2}-x y^{\prime}=0\)
- D \(x^{2} y^{\prime}+x y^{\prime \prime}-3 y=0\)
Where \(y^{\prime} \equiv \frac{d y}{d x}, y^{\prime \prime} \equiv \frac{d^{2} y}{d x^{2}}\)
Answer & Solution
Correct Answer
(B) \(x y y^{\prime \prime}+x y^{\prime 2}-y y^{\prime}=0\)
Step-by-step Solution
Detailed explanation
equation of ellipse centred at origin and have axes as the coordinate axes is \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) \(\Rightarrow \frac{x}{a^{2}}+\frac{y y^{\prime}}{b^{2}}=0\) \(\Rightarrow \quad \frac{-b^{2}}{a^{2}}=\frac{y y^{\prime}}{x}\)…
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