ODE
\[ y''(x)+y(x)^3 y'(x)=y(x) y'(x) \sqrt {4 y'(x)+y(x)^4} \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.36341 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \sqrt {2} e^{c_1} \tan \left (2 \sqrt {2} e^{3 c_1} \left (c_2+x\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.194 (sec), leaf count = 41
\[ \left \{ {{\it Artanh} \left ( y \left ( x \right ) {\it \_C1} \right ) \left ( {{\it \_C1}}^{-2} \right ) ^{-{\frac {3}{2}}}}-x-{\it \_C2}=0,{\arctan \left ( y \left ( x \right ) {\it \_C1} \right ) \left ( {{\it \_C1}}^{-2} \right ) ^{-{\frac {3}{2}}}}-x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[y[x]^3*y'[x] + y''[x] == y[x]*y'[x]*Sqrt[y[x]^4 + 4*y'[x]],y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[2]*E^C[1]*Tan[2*Sqrt[2]*E^(3*C[1])*(x + C[2])]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+y(x)^3*diff(y(x),x) = y(x)*diff(y(x),x)*(y(x)^4+4*diff(y(x),x))^(1/2), y(x),'implicit')
Maple raw output
1/(1/_C1^2)^(3/2)*arctan(y(x)*_C1)-x-_C2 = 0, 1/(1/_C1^2)^(3/2)*arctanh(y(x)*_C1)-x-_C2 = 0