Question
Download Solution PDFWhat is the differential equation of \(\rm y = A- \frac{B}{x}\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
\(\rm \frac{d}{dx} x^{n} = nx^{n - 1}\)
Calculation:
We have \(\rm y = A -\frac{B}{x}\)
On differentiating the above equation with respect to x, we get
⇒ \(\rm y_{1} = \frac{B}{x^{2}}\)
⇒ x2 \(\rm y_{1} = B\)
again differentiate with respect to x
⇒ \(\rm x^{2} y_{2} + 2x y_{1} = 0\)
⇒ x\(\rm (x y_{2}+ 2 y_{1}) = 0\)
⇒ \(\rm (x y_{2}+ 2 y_{1}) = 0\)
∴ The differential equation of \(\rm y = A -\frac{B}{x}\) is \(\rm (x y_{2}+ 2 y_{1}) = 0\).
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