\[ y''(x)=-\frac {y'(x) \left (-\phi ''(x)-\phi (x) \phi '(x)+\phi \left (x^3\right )\right )}{\phi '(x)+\phi (x)^2}-\frac {y(x) \left (-\phi (x) \phi ''(x)+\phi (x)^2 \left (-\phi '(x)\right )+\phi '(x)^2\right )}{\phi '(x)+\phi (x)^2} \] ✗ Mathematica : cpu = 0.65428 (sec), leaf count = 0
DSolve[Derivative[2][y][x] == -((Derivative[1][y][x]*(phi[x^3] - phi[x]*Derivative[1][phi][x] - Derivative[2][phi][x]))/(phi[x]^2 + Derivative[1][phi][x])) - (y[x]*(-(phi[x]^2*Derivative[1][phi][x]) + Derivative[1][phi][x]^2 - phi[x]*Derivative[2][phi][x]))/(phi[x]^2 + Derivative[1][phi][x]),y[x],x]
, could not solve
DSolve[Derivative[2][y][x] == -((Derivative[1][y][x]*(phi[x^3] - phi[x]*Derivative[1][phi][x] - Derivative[2][phi][x]))/(phi[x]^2 + Derivative[1][phi][x])) - (y[x]*(-(phi[x]^2*Derivative[1][phi][x]) + Derivative[1][phi][x]^2 - phi[x]*Derivative[2][phi][x]))/(phi[x]^2 + Derivative[1][phi][x]), y[x], x]
✗ Maple : cpu = 0. (sec), leaf count = 0
dsolve(diff(diff(y(x),x),x) = -(phi(x^3)-phi(x)*diff(phi(x),x)-diff(diff(phi(x),x),x))/(diff(phi(x),x)+phi(x)^2)*diff(y(x),x)-(diff(phi(x),x)^2-phi(x)^2*diff(phi(x),x)-phi(x)*diff(diff(phi(x),x),x))/(diff(phi(x),x)+phi(x)^2)*y(x),y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \mathit {DESol}\left (\left \{\frac {\left (\left (\frac {d}{d x}\phi \left (x \right )\right )^{2}-\phi \left (x \right )^{2} \left (\frac {d}{d x}\phi \left (x \right )\right )-\phi \left (x \right ) \left (\frac {d^{2}}{d x^{2}}\phi \left (x \right )\right )\right ) \textit {\_Y} \left (x \right )}{\frac {d}{d x}\phi \left (x \right )+\phi \left (x \right )^{2}}+\frac {\left (\phi \left (x^{3}\right )-\phi \left (x \right ) \left (\frac {d}{d x}\phi \left (x \right )\right )-\frac {d^{2}}{d x^{2}}\phi \left (x \right )\right ) \left (\frac {d}{d x}\textit {\_Y} \left (x \right )\right )}{\frac {d}{d x}\phi \left (x \right )+\phi \left (x \right )^{2}}+\frac {d^{2}}{d x^{2}}\textit {\_Y} \left (x \right )\right \}, \left \{\textit {\_Y} \left (x \right )\right \}\right )\]