\[ h(y(x))^2 \left (-j\left (x,\frac {y'(x)}{h(y(x))}\right )\right )+h(y(x)) y''(x)-h(y(x)) y'(x)^2=0 \] ✗ Mathematica : cpu = 1.29788 (sec), leaf count = 0
DSolve[-(h[y[x]]^2*j[x, Derivative[1][y][x]/h[y[x]]]) - h[y[x]]*Derivative[1][y][x]^2 + h[y[x]]*Derivative[2][y][x] == 0,y[x],x]
, could not solve
DSolve[-(h[y[x]]^2*j[x, Derivative[1][y][x]/h[y[x]]]) - h[y[x]]*Derivative[1][y][x]^2 + h[y[x]]*Derivative[2][y][x] == 0, y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(h(y(x))*diff(diff(y(x),x),x)-D(h)(y(x))*diff(y(x),x)^2-h(y(x))^2*j(x,diff(y(x),x)/h(y(x)))=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \operatorname {RootOf}\left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}-\left (\int _{}^{\textit {\_Z}}\frac {1}{h \left (\textit {\_f} \right )}d \textit {\_f} \right )\right )\:\& \text {where}\:\left [\left \{\frac {d}{d \textit {\_a}}\textit {\_}b\left (\textit {\_a} \right )=j \left (\textit {\_a} , \textit {\_}b\left (\textit {\_a} \right )\right )\right \}, \left \{\textit {\_a} =x , \textit {\_}b\left (\textit {\_a} \right )=\frac {\frac {d}{d x}y \left (x \right )}{h \left (y \left (x \right )\right )}\right \}, \left \{x =\textit {\_a} , y \left (x \right )=\operatorname {RootOf}\left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}-\left (\int _{}^{\textit {\_Z}}\frac {1}{h \left (\textit {\_f} \right )}d \textit {\_f} \right )\right )\right \}\right ]\]