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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
MCQ
$y = \frac{x}{{x + 1}}$ is a solution of the differential equation
  • A
    ${y^2}\frac{{dy}}{{dx}} = {x^2}$
  • ✓
    ${x^2}\frac{{dy}}{{dx}} = {y^2}$
  • C
    $y\frac{{dy}}{{dx}} = x$
  • D
    $x\frac{{dy}}{{dx}} = y$
✓

Answer

Correct option: B.
${x^2}\frac{{dy}}{{dx}} = {y^2}$
b
(b) $y = \frac{x}{{x + 1}} \Rightarrow \frac{1}{y} = 1 + \frac{1}{x}$

$ - \frac{1}{{{y^2}}}\frac{{dy}}{{dx}} = 0 - \frac{1}{{{x^2}}}$ ==> ${x^2}\frac{{dy}}{{dx}} = {y^2}$.

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