3.375   ODE No. 375

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

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

Mathematica: cpu = 0.062508 (sec), leaf count = 71 \[ \left \{\left \{y(x)\to \frac {1}{2} \left (-\frac {\left (a^2-4 b x\right )^{3/2}}{6 b}-a x\right )+c_1\right \},\left \{y(x)\to \frac {1}{2} \left (\frac {\left (a^2-4 b x\right )^{3/2}}{6 b}-a x\right )+c_1\right \}\right \} \]

Maple: cpu = 0.468 (sec), leaf count = 49 \[ \left \{ y \left ( x \right ) =-{\frac {ax}{2}}-{\frac {1}{12\,b} \left ( {a}^{2}-4\,bx \right ) ^{{\frac {3}{2}}}}+{\it \_C1},y \left ( x \right ) =-{\frac {ax}{2}}+{\frac {1}{12\,b} \left ( {a}^{2}-4\,bx \right ) ^{{\frac {3}{2}}}}+{\it \_C1} \right \} \]