Question

The differential equation of the family of curves $v=\frac{A}{r}+B$,where $A$ and $B$ are arbitrary constant, is

• A. $\frac{d^{}v}{{dr}^{}}+\frac{1}{r}\frac{dv}{dr}=0$
• B. $\frac{d^{2}v}{{dr}^2}+\frac{1}{r}\frac{dv}{dr}=0$
• C. $\frac{d^{2}v}{{dr}^2}+\frac{2}{r}\frac{dv}{dr}=0$
• D. $noneofthese$

Answer 1

The correct option is C $\frac{d^{2}v}{{dr}^2}+\frac{2}{r}\frac{dv}{dr}=0$

$\Rightarrow \frac{dv}{dr}=-\frac{A}{r^2}$

$\Rightarrow \frac{d^{2}v}{d{r}^2}=\frac{2A}{r^3}$

$\Rightarrow \frac{d^{2}v}{d{r}^2}=\frac{2}{r^3}(-r^2\frac{dv}{dr})$

$\Rightarrow \frac{d^{2}v}{d{r}^2}+\frac{2}{r}\frac{dv}{dr}=0$