3.126   ODE No. 126

\[ \boxed { x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) f \left ( xy \left ( x \right ) \right ) =0} \]

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

Mathematica: cpu = 15.028909 (sec), leaf count = 112 \[ \text {Solve}\left [\int _1^{y(x)} \left (\frac {1}{K[2] (-f(x K[2])-1)}-\int _1^x \left (\frac {f'(K[1] K[2])}{f(K[1] K[2])+1}-\frac {f(K[1] K[2]) f'(K[1] K[2])}{(f(K[1] K[2])+1)^2}\right ) \, dK[1]\right ) \, dK[2]+\int _1^x \frac {f(y(x) K[1])}{K[1] (f(y(x) K[1])+1)} \, dK[1]=c_1,y(x)\right ] \]

Maple: cpu = 0.016 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) ={\frac {1}{x}{\it RootOf} \left ( -\ln \left ( x \right ) +{\it \_C1}+\int ^{{\it \_Z}}\!{\frac {1}{{\it \_a} \, \left ( 1+f \left ( {\it \_a} \right ) \right ) }}{d{\it \_a}} \right ) } \right \} \]