Is there any way to solve the following system of non-linear differential equations exactly?


$x'(t) = x\times(y - \frac{1}{3(t + C)})$


$y'(t) = -\frac{1}{3}x^2 - \frac{y}{t + C}$


Here $x$ and $y$ are functions of $t$, and $C$ is some constant. 



Is this non-linear system of differential equations tractable by other means than numeric approximation and dynamic analysis?
By changing the origin of time, we may assume $C=0$. One special family of 
solutions is $x = 0, y = c/t$. But the general solution is


$$\eqalign{x(t) &= 12\,{\frac {a b^2{t}^{b-1}}{{a}^{2}{t}^{2\,b}+
12\,{b}^{2}}}
\cr
y(t) &={\frac {144\,{b}^{5}- a^4 \left( b+2/3 \right) {t}^{4\,b}-
16\,a^2 b^2 {t}^{2\,b}-96\,{b}^{4}}{ \left( a^2 {t}^{2\,b}+
12\,{b}^{2} \right) ^{2}t}}
 }$$


