8.3.7 Systems of ordinary differential equations

Problem: Find the particular solution of the system of linear differential equations: \[ \left\{\begin{array}{l} \dot{x}=\frac{x}{x+3 y} \\ \dot{y}=\frac{3 y}{x+3 y} \end{array} \quad x(1)=y(1)=1 .\right. \]