ODE No. 1577

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

\[ f''(x) y''(x)+2 y^{(3)}(x) f'(x)+f(x) y^{(4)}(x)=0 \] Mathematica : cpu = 1.1421 (sec), leaf count = 44

\[\left \{\left \{y(x)\to \int _1^x \left (\int _1^{K[2]} \left (\frac {c_1}{f(K[1])}+\frac {c_2 K[1]}{f(K[1])}\right ) \, dK[1]\right ) \, dK[2]+c_4 x+c_3\right \}\right \}\] Maple : cpu = 0.012 (sec), leaf count = 21

\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{3}}{6}}+{\frac {{\it \_C2}\,{x}^{2}}{2}}+{\it \_C3}\,x+{\it \_C4} \right \} \]