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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
MCQ
The solution of $\frac{{dy}}{{dx}} = {\left( {\frac{y}{x}} \right)^{1/3}}$ is
  • A
    ${x^{2/3}} + {y^{2/3}} = c$
  • B
    ${x^{1/3}} + {y^{1/3}} = c$
  • ✓
    ${y^{2/3}} - {x^{2/3}} = c$
  • D
    ${y^{1/3}} - {x^{1/3}} = c$
✓

Answer

Correct option: C.
${y^{2/3}} - {x^{2/3}} = c$
c
(c) $\frac{{dy}}{{dx}} = {\left( {\frac{y}{x}} \right)^{1/3}}$ ==> $\frac{{dy}}{{dx}} = \frac{{{y^{1/3}}}}{{{x^{1/3}}}}$ ==> $\frac{{dy}}{{{y^{1/3}}}} = \frac{{dx}}{{{x^{1/3}}}}$

Integrating both sides, $\frac{{{y^{2/3}}}}{{2/3}} = \frac{{{x^{2/3}}}}{{2/3}} + c$

$\frac{3}{2} \cdot {y^{2/3}} = \frac{3}{2}{x^{2/3}} + c$ ==> ${y^{2/3}} - {x^{2/3}} = c$.

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