8.162   ODE No. 1752

\[ \boxed { 4\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) -5\, \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+a \left ( y \left ( x \right ) \right ) ^{2}=0} \]

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

Mathematica: cpu = 0.129016 (sec), leaf count = 26 \[ \left \{\left \{y(x)\to c_2 \text {sech}^4\left (\frac {1}{4} \sqrt {a} \left (x-4 c_1\right )\right )\right \}\right \} \]

Maple: cpu = 1.575 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) =16\,{\frac { \left ( {{\rm e}^{1/4\,\sqrt {a}x}} \right ) ^{4}{a}^{2}}{ \left ( {{\rm e}^{1/2\,\sqrt {a}x}}{\it \_C1}-{\it \_C2} \right ) ^{4}}} \right \} \]