4.340   ODE No. 1340

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =2\,{\frac { \left ( ax+2\,b \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{x \left ( ax+b \right ) }}-{\frac { \left ( 2\,ax+6\,b \right ) y \left ( x \right ) }{ \left ( ax+b \right ) {x}^{2}}}=0} \]

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

Mathematica: cpu = 0.035005 (sec), leaf count = 32 \[ \left \{\left \{y(x)\to \frac {c_2 x^3}{a x+b}+\frac {c_1 x^2}{a x+b}\right \}\right \} \]

Maple: cpu = 0.015 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{2}}{ax+b}}+{ \frac {{\it \_C2}\,{x}^{3}}{ax+b}} \right \} \]