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 = 0.625101 (sec), leaf count = 151
\[\left \{\left \{y(x)\to -\frac {1}{2} (\cosh (c_1)+\sinh (c_1)) (\tan ((x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))+i) (\cos (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))+i \sin (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))-1)\right \},\left \{y(x)\to -\frac {1}{2} (\cosh (c_1)+\sinh (c_1)) (\cosh (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))+\sinh (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))-1) (-1+\tanh ((x+c_2) (\cosh (3 c_1)+\sinh (3 c_1))))\right \}\right \}\]
Maple ✓
cpu = 0.641 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {\tan \left (\frac {x +\textit {\_C2}}{\left (\textit {\_C1}^{2}\right )^{\frac {3}{2}}}\right )}{\textit {\_C1}}, y \left (x \right ) = \frac {\tanh \left (\frac {x +\textit {\_C2}}{\left (\textit {\_C1}^{2}\right )^{\frac {3}{2}}}\right )}{\textit {\_C1}}\right ]\] 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] -> -1/2*((-1 + Cos[2*(x + C[2])*(Cosh[3*C[1]] + Sinh[3*C[1]])] + I*Sin[2*(x + C[2])*(Cosh[3*C[1]] + Sinh[3*C[1]])])*(Cosh[C[1]] + Sinh[C[1]])*(I + Tan[(x + C[2])*(Cosh[3*C[1]] + Sinh[3*C[1]])]))}, {y[x] -> -1/2*((Cosh[C[1]] + Sinh[C[1]])*(-1 + Cosh[2*(x + C[2])*(Cosh[3*C[1]] + Sinh[3*C[1]])] + Sinh[2*(x + C[2])*(Cosh[3*C[1]] + Sinh[3*C[1]])])*(-1 + Tanh[(x + C[2])*(Cosh[3*C[1]] + Sinh[3*C[1]])]))}}
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))
Maple raw output
[y(x) = tan((x+_C2)/(_C1^2)^(3/2))/_C1, y(x) = tanh((x+_C2)/(_C1^2)^(3/2))/_C1]