ODE
\[ 2 y'(x)^2+2 (6 y(x)-1) y'(x)+3 y(x) (6 y(x)-1)=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.0566033 (sec), leaf count = 69
\[\left \{\left \{y(x)\to -\frac {1}{6} e^{3 c_1-3 x} \left (e^{3 c_1}-2 e^{3 x/2}\right )\right \},\left \{y(x)\to \frac {1}{6} e^{-3 \left (2 c_1+x\right )} \left (2 e^{3 c_1+\frac {3 x}{2}}-1\right )\right \}\right \}\]
Maple ✓
cpu = 0.051 (sec), leaf count = 51
\[ \left \{ x+{\frac {\ln \left ( y \left ( x \right ) \right ) }{3}}-{\frac {2}{3}{\it Artanh} \left ( \sqrt {-6\,y \left ( x \right ) +1} \right ) }-{\it \_C1}=0,x+{\frac {\ln \left ( y \left ( x \right ) \right ) }{3}}+{\frac {2}{3}{\it Artanh} \left ( \sqrt {-6\,y \left ( x \right ) +1} \right ) }-{\it \_C1}=0,y \left ( x \right ) ={\frac {1}{6}} \right \} \] Mathematica raw input
DSolve[3*y[x]*(-1 + 6*y[x]) + 2*(-1 + 6*y[x])*y'[x] + 2*y'[x]^2 == 0,y[x],x]
Mathematica raw output
{{y[x] -> -(E^(-3*x + 3*C[1])*(-2*E^((3*x)/2) + E^(3*C[1])))/6}, {y[x] -> (-1 + 2*E^((3*x)/2 + 3*C[1]))/(6*E^(3*(x + 2*C[1])))}}
Maple raw input
dsolve(2*diff(y(x),x)^2+2*(6*y(x)-1)*diff(y(x),x)+3*y(x)*(6*y(x)-1) = 0, y(x),'implicit')
Maple raw output
y(x) = 1/6, x+1/3*ln(y(x))-2/3*arctanh((-6*y(x)+1)^(1/2))-_C1 = 0, x+1/3*ln(y(x))+2/3*arctanh((-6*y(x)+1)^(1/2))-_C1 = 0