# Thread: seperable differential equation

1. ## seperable differential equation

$\dfrac{dx}{dt}$ = $x^2 + \dfrac{1}{81}$

x(0) = 5

the answer i got was
$
\dfrac{1}{9} tan( \dfrac{t}{9} + \dfrac{13.94}{9})$

but seems to be wrong and i cant seem to figure out what im doing wrong

2. $\dfrac{dx}{dt} = x^2 + \frac{1}{81} \Rightarrow \dfrac{dx}{x^2 + \frac{1}{81}}= dt \Rightarrow \int\!\dfrac{dx}{x^2 + \frac{1}{81}}= \int\!\,dt \Rightarrow 9 \tan^{-1} (9x) = t + c \Rightarrow 9\tan^{-1} 45 = c \dots$
So it appears that your solution is correct.