JEE Mains · Maths · STD 12 - 9. differential equations
If a curve passes through the point \((1, -2)\) and has slope of the tangent at any point \((x,y)\) on it as \(\frac{{{x^2} - 2y}}{x}\) then the curve also passes through the point
- A \((3, 0)\)
- B \((\sqrt 3,0)\)
- C \((-1, 2)\)
- D \((-\sqrt 2, 1)\)
Answer & Solution
Correct Answer
(B) \((\sqrt 3,0)\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=\frac{x^{2}-2 y}{x} \quad(\text { Given })\) \(\frac{d y}{d x}+2 \frac{y}{x}=x\) \(\mathrm{IF}_{.}=\mathrm{e}^{\int \frac{2}{\mathrm{x}} \mathrm{dx}}=\mathrm{x}^{2}\) \(\therefore y \cdot x^{2}=\int x \cdot x^{2} d x+C\) \(=\frac{x^{4}}{y}+C\) Hence \(b\)…
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