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 = 1.31354 (sec), leaf count = 24
\[\text {Solve}\left [y(x)^2+x=c_2 e^{e^{-c_1} y(x)},y(x)\right ]\]
Maple ✓
cpu = 0.595 (sec), leaf count = 23
\[\left [\frac {-\textit {\_C1} y \left (x \right )+\ln \left (x +y \left (x \right )^{2}\right )+\textit {\_C2} +2}{y \left (x \right )} = 0\right ]\] 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))
Maple raw output
[1/y(x)*(-_C1*y(x)+ln(x+y(x)^2)+_C2+2) = 0]