Differential Equations Question 117
Question: The differential equation of the family of curves $ v=\frac{A}{r}+B, $ where A and B are arbitrary constants, is
Options:
A) $ \frac{d^{2}v}{dr^{2}}+\frac{1}{r}\frac{dv}{dr}=0 $
B) $ \frac{d^{2}v}{dr^{2}}-\frac{2}{r}\frac{dv}{dr}=0 $
C) $ \frac{d^{2}v}{dr^{2}}+\frac{2}{r}\frac{dv}{dr}=0 $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dv}{dr}=-\frac{A}{r^{2}}+0 $
Therefore $ \frac{d^{2}v}{dr^{2}}=\frac{2A}{r^{3}} $
Therefore $ \frac{d^{2}v}{dr^{2}}=\frac{2}{r}( \frac{A}{r^{2}} ) $
Therefore $ \frac{d^{2}v}{dr^{2}}=\frac{2}{r}( -\frac{dv}{dr} ) $
Therefore $ \frac{d^{2}v}{dr^{2}}+\frac{2}{r}\frac{dv}{dr}=0 $ .
BETA
