If solution of differential equation dy dx = 1 + x 2y is a conic … - Vidyadip

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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