2.1695   ODE No. 1695

\[ y(x) y''(x)-a x=0 \] Mathematica : cpu = 15.2584 (sec), leaf count = 0


, could not solve

DSolve[-(a*x) + y[x]*Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 0. (sec), leaf count = 0


, result contains DESol or ODESolStruc

\[y \relax (x ) = \left (\textit {\_a} \left ({\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}\right )^{\frac {3}{2}}\right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\frac {\left (3 \textit {\_a}^{2}-4 a \right ) \textit {\_}b\left (\textit {\_a} \right )^{3}}{4 \textit {\_a}}+2 \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =\frac {y \relax (x )}{x^{\frac {3}{2}}}, \textit {\_}b\left (\textit {\_a} \right )=-\frac {2 x^{\frac {3}{2}}}{-2 x \left (\frac {d}{d x}y \relax (x )\right )+3 y \relax (x )}\right \}, \left \{x ={\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}, y \relax (x )=\textit {\_a} \left ({\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}\right )^{\frac {3}{2}}\right \}\right ]\]