ODE No. 1694

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

\[ y(x) y''(x)-a=0 \] Mathematica : cpu = 0.199633 (sec), leaf count = 115

\[\left \{\left \{y(x)\to \exp \left (\frac {-c_1-2 a \text {erf}^{-1}\left (-i \sqrt {\frac {2}{\pi }} \sqrt {a e^{\frac {c_1}{a}} \left (c_2+x\right ){}^2}\right ){}^2}{2 a}\right )\right \},\left \{y(x)\to \exp \left (\frac {-c_1-2 a \text {erf}^{-1}\left (i \sqrt {\frac {2}{\pi }} \sqrt {a e^{\frac {c_1}{a}} \left (c_2+x\right ){}^2}\right ){}^2}{2 a}\right )\right \}\right \}\] Maple : cpu = 0.182 (sec), leaf count = 54

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