8.117   ODE No. 1707

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

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

Mathematica: cpu = 0.072509 (sec), leaf count = 31 \[ \left \{\left \{y(x)\to c_2 e^{-\frac {b x}{a}-\frac {c_1 e^{-a x}}{a}}\right \}\right \} \]

Maple: cpu = 1.545 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) ={1{{\rm e}^{{\frac {{{\rm e}^{-ax}}{\it \_C1}}{a}}}}{{\rm e}^{{\frac {b}{{a}^{2}}}}} \left ( {{\rm e}^{{\frac { bx}{a}}}} \right ) ^{-1} \left ( {{\rm e}^{{\frac {{\it \_C2}}{a}}}} \right ) ^{-1}} \right \} \]