2.1814   ODE No. 1814

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

\[ a h(y(x)) y'(x)^2+h(y(x)) y''(x)+j(y(x))=0 \] Mathematica : cpu = 0.341949 (sec), leaf count = 120

\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {e^{a K[2]}}{\sqrt {c_1+2 \int _1^{K[2]}-\frac {e^{2 a K[1]} j(K[1])}{h(K[1])}dK[1]}}dK[2]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {e^{a K[3]}}{\sqrt {c_1+2 \int _1^{K[3]}-\frac {e^{2 a K[1]} j(K[1])}{h(K[1])}dK[1]}}dK[3]\& \right ][x+c_2]\right \}\right \}\] Maple : cpu = 0.81 (sec), leaf count = 87

\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{ \left ( h \left ( {\it \_b} \right ) \right ) ^{-a}}{\frac {1}{\sqrt {-2\,\int \!{\frac { \left ( \left ( h \left ( {\it \_b} \right ) \right ) ^{a} \right ) ^{2}}{h \left ( {\it \_b} \right ) }}\,{\rm d}{\it \_b}+{\it \_C1}}}}}{d{\it \_b}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{ \left ( h \left ( {\it \_b} \right ) \right ) ^{-a}}{\frac {1}{\sqrt {-2\,\int \!2\,{\frac { \left ( \left ( h \left ( {\it \_b} \right ) \right ) ^{a} \right ) ^{2}}{h \left ( {\it \_b} \right ) }}\,{\rm d}{\it \_b}+{\it \_C1}}}}}{d{\it \_b}}-x-{\it \_C2}=0 \right \} \]