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प्रश्न
The solution of x2 + y2 \[\frac{dy}{dx}\]= 4, is
विकल्प
x2 + y2 = 12x + C
x2 + y2 = 3x + C
x3 + y3 = 3x + C
x3 + y3 = 12x + C
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उत्तर
x3 + y3 = 12x + C
We have,
\[ x^2 + y^2 \frac{dy}{dx} = 4\]
\[ \Rightarrow y^2 \frac{dy}{dx} = 4 - x^2 \]
\[ \Rightarrow y^2 dy = \left( 4 - x^2 \right)dx\]
Integrating both sides, we get
\[\int y^2 dy = \int\left( 4 - x^2 \right)dx\]
\[ \Rightarrow \frac{y^3}{3} = 4x - \frac{x^3}{3} + D\]
\[ \Rightarrow y^3 = 12x - x^3 + 3D\]
\[ \Rightarrow x^3 + y^3 = 12x + C,\text{ where }C = 3D\]
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