4.253   ODE No. 1253

\[ \boxed { x \left ( 1+x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 3\,x+2 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.025003 (sec), leaf count = 34 \[ \left \{\left \{y(x)\to \frac {\sqrt {2} c_1}{x}+\frac {c_2 \log (2 x+2)}{\sqrt {2} x}\right \}\right \} \]

Maple: cpu = 0.0 (sec), leaf count = 16 \[ \left \{ y \left ( x \right ) ={\frac {\ln \left ( 1+x \right ) {\it \_C1 }+{\it \_C2}}{x}} \right \} \]