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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
MCQ
If solution of differential equation $\frac{{dy}}{{dx}} = \frac{{1 + x}}{{2y}}$ is a conic passing through point $(1,1),$ then its eccentricity, is-
  • A
    $0$
  • ✓
    $\sqrt {\frac{3}{2}} $
  • C
    $1$
  • D
    $\sqrt {\frac{5}{3}} $
✓

Answer

Correct option: B.
$\sqrt {\frac{3}{2}} $
b
$\int 2 y d y=\int(1+x) d x \Rightarrow \frac{(x+1)^{2}}{2}-\frac{y^{2}}{1}=1$

$\Rightarrow \mathrm{e}=\sqrt{1+\frac{1}{2}}=\sqrt{\frac{3}{2}}$

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