ODE No. 1641

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

\[ g(x) y'(x)+h(y(x)) y'(x)^2+y''(x)=0 \] Mathematica : cpu = 1.98266 (sec), leaf count = 57

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} e^{-\int _1^{K[4]} -h(K[1]) \, dK[1]} \, dK[4]\& \right ]\left [\int _1^x c_1 \left (-e^{-\int _1^{K[5]} g(K[2]) \, dK[2]}\right ) \, dK[5]+c_2\right ]\right \}\right \}\] Maple : cpu = 0.043 (sec), leaf count = 29

\[ \left \{ \int ^{y \left ( x \right ) }\!{{\rm e}^{\int \!h \left ( {\it \_b} \right ) \,{\rm d}{\it \_b}}}{d{\it \_b}}-{\it \_C1}\,\int \!{{\rm e}^{-\int \!g \left ( x \right ) \,{\rm d}x}}\,{\rm d}x-{\it \_C2}=0 \right \} \]