ODE
\[ y''(x)+4 y'(x)^3+2 y'(x)=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0729568 (sec), leaf count = 95
\[\left \{\left \{y(x)\to c_2-\frac {\tan ^{-1}\left (\frac {e^{-c_1} \sqrt {e^{4 x}-2 e^{2 c_1}}}{\sqrt {2}}\right )}{2 \sqrt {2}}\right \},\left \{y(x)\to \frac {\tan ^{-1}\left (\frac {e^{-c_1} \sqrt {e^{4 x}-2 e^{2 c_1}}}{\sqrt {2}}\right )}{2 \sqrt {2}}+c_2\right \}\right \}\]
Maple ✓
cpu = 0.245 (sec), leaf count = 49
\[ \left \{ y \left ( x \right ) =-{\frac {\sqrt {2}}{4}\arctan \left ( {\frac {1}{2}\sqrt {2\,{{\rm e}^{4\,x}}{\it \_C1}-4}} \right ) }+{\it \_C2},y \left ( x \right ) ={\frac {\sqrt {2}}{4}\arctan \left ( {\frac {1}{2}\sqrt {2\,{{\rm e}^{4\,x}}{\it \_C1}-4}} \right ) }+{\it \_C2} \right \} \] Mathematica raw input
DSolve[2*y'[x] + 4*y'[x]^3 + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -ArcTan[Sqrt[E^(4*x) - 2*E^(2*C[1])]/(Sqrt[2]*E^C[1])]/(2*Sqrt[2]) + C[2]}, {y[x] -> ArcTan[Sqrt[E^(4*x) - 2*E^(2*C[1])]/(Sqrt[2]*E^C[1])]/(2*Sqrt[2]) + C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+2*diff(y(x),x)+4*diff(y(x),x)^3 = 0, y(x),'implicit')
Maple raw output
y(x) = 1/4*2^(1/2)*arctan(1/2*(2*exp(4*x)*_C1-4)^(1/2))+_C2, y(x) = -1/4*2^(1/2)*arctan(1/2*(2*exp(4*x)*_C1-4)^(1/2))+_C2