3.223   ODE No. 223

\[ \boxed { \left ( 2\,y \left ( x \right ) -x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) -2\,x=0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 0.025003 (sec), leaf count = 55 \[ \left \{\left \{y(x)\to \frac {1}{2} \left (x-\sqrt {5 x^2-4 e^{c_1}}\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {5 x^2-4 e^{c_1}}+x\right )\right \}\right \} \]

Maple: cpu = 0.109 (sec), leaf count = 53 \[ \left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( {\frac {{ \it \_C1}\,x}{2}}-{\frac {1}{2}\sqrt {5\,{{\it \_C1}}^{2}{x}^{2}+4}} \right ) },y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( {\frac {{ \it \_C1}\,x}{2}}+{\frac {1}{2}\sqrt {5\,{{\it \_C1}}^{2}{x}^{2}+4}} \right ) } \right \} \]