if the curve $y = g (x)$ ,passing through $(- 1, - 2)$ and satisfies the differential equation the $g (x)$ equals

\frac{2 + x^{2}}{2 x}

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\frac{x^{2} + 1}{3 - x^{2}}

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\frac{2 x}{2 - x^{2}}

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\frac{x}{1 - 3 x^{2}}

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Solution

The correct option is C $\frac{2 x}{2 - x^{2}}$
$y = g (x)$
A) Substituting $x = - 1$ in $y = \frac{2 + x^{2}}{2 x}$ we get $y = - \frac{3}{2}$
B) Substituting $x = - 1$ in $y = \frac{x^{2} + 1}{3 - x^{2}}$ we get $y = 1$
C) Substituting $x = - 1$ in $y = \frac{2 x}{2 + x^{2}}$ we get $y = - 2$
D) Substituting $x = - 1$ in $y = \frac{x}{1 - 3 x^{2}}$ we get $y = - \frac{1}{2}$

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if the curve y=g(x) ,passing through (−1,−2) and satisfies the differential equation the g(x) equals

The correct option is C 2x2−x2y=g(x)A) Substituting x=−1 in y=2+x22x we get y=−32B) Substituting x=−1 in y=x2+13−x2 we get y=1C) Substituting x=−1 in y=2x2+x2 we get y=−2D) Substituting x=−1 in y=x1−3x2 we get y=−12

if the curve $y = g (x)$ ,passing through $(- 1, - 2)$ and satisfies the differential equation the $g (x)$ equals