ODE
\[ \left (y(x)^2+x\right ) y''(x)=2 \left (x-y(x)^2\right ) y'(x)^3-y'(x) \left (4 y(x) y'(x)+1\right ) \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 1.39674 (sec), leaf count = 24
\[\text {Solve}\left [y(x)^2+x=c_2 e^{e^{-c_1} y(x)},y(x)\right ]\]
Maple ✓
cpu = 0.154 (sec), leaf count = 23
\[ \left \{ {\frac {-{\it \_C1}\,y \left ( x \right ) +\ln \left ( x+ \left ( y \left ( x \right ) \right ) ^{2} \right ) +{\it \_C2}+2}{y \left ( x \right ) }}=0 \right \} \] Mathematica raw input
DSolve[(x + y[x]^2)*y''[x] == 2*(x - y[x]^2)*y'[x]^3 - y'[x]*(1 + 4*y[x]*y'[x]),y[x],x]
Mathematica raw output
Solve[x + y[x]^2 == E^(y[x]/E^C[1])*C[2], y[x]]
Maple raw input
dsolve((x+y(x)^2)*diff(diff(y(x),x),x) = 2*(x-y(x)^2)*diff(y(x),x)^3-diff(y(x),x)*(1+4*y(x)*diff(y(x),x)), y(x),'implicit')
Maple raw output
1/y(x)*(-_C1*y(x)+ln(x+y(x)^2)+_C2+2) = 0