ODE
\[ 2 y(x) y''(x)=6 y'(x)^2+\left (1-3 y(x)^2\right ) y(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 1.27632 (sec), leaf count = 217
\[\left \{\left \{y(x)\to -\frac {2 i e^{\frac {1}{2} i \left (c_2+x\right )}}{\sqrt {-12 e^{i \left (c_2+x\right )}+e^{2 i \left (c_2+x\right )}+16 c_1+36}}\right \},\left \{y(x)\to \frac {2 i e^{\frac {1}{2} i \left (c_2+x\right )}}{\sqrt {-12 e^{i \left (c_2+x\right )}+e^{2 i \left (c_2+x\right )}+16 c_1+36}}\right \},\left \{y(x)\to -\frac {2 i e^{\frac {1}{2} i \left (c_2+x\right )}}{\sqrt {4 \left (4 c_1+9\right ) e^{2 i \left (c_2+x\right )}-12 e^{i \left (c_2+x\right )}+1}}\right \},\left \{y(x)\to \frac {2 i e^{\frac {1}{2} i \left (c_2+x\right )}}{\sqrt {4 \left (4 c_1+9\right ) e^{2 i \left (c_2+x\right )}-12 e^{i \left (c_2+x\right )}+1}}\right \}\right \}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 25
\[ \left \{ {\frac {1+ \left ( {\it \_C1}\,\sin \left ( x \right ) +{\it \_C2}\,\cos \left ( x \right ) -3 \right ) \left ( y \left ( x \right ) \right ) ^{2}}{ \left ( y \left ( x \right ) \right ) ^{2}}}=0 \right \} \] Mathematica raw input
DSolve[2*y[x]*y''[x] == y[x]^2*(1 - 3*y[x]^2) + 6*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> ((-2*I)*E^((I/2)*(x + C[2])))/Sqrt[36 - 12*E^(I*(x + C[2])) + E^((2*I)*(x + C[2])) + 16*C[1]]}, {y[x] -> ((2*I)*E^((I/2)*(x + C[2])))/Sqrt[36 - 12*E^(I*(x + C[2])) + E^((2*I)*(x + C[2])) + 16*C[1]]}, {y[x] -> ((-2*I)*E^((I/2)*(x + C[2])))/Sqrt[1 - 12*E^(I*(x + C[2])) + 4*E^((2*I)*(x + C[2]))*(9 + 4*C[1])]}, {y[x] -> ((2*I)*E^((I/2)*(x + C[2])))/Sqrt[1 - 12*E^(I*(x + C[2])) + 4*E^((2*I)*(x + C[2]))*(9 + 4*C[1])]}}
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = 6*diff(y(x),x)^2+(1-3*y(x)^2)*y(x)^2, y(x),'implicit')
Maple raw output
(1+(_C1*sin(x)+_C2*cos(x)-3)*y(x)^2)/y(x)^2 = 0