ODE
\[ 2 y(x) y''(x)=y'(x)^2+8 y(x)^3 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.453775 (sec), leaf count = 77
\[\left \{\left \{y(x)\to -\frac {1}{2} i \sqrt {c_1} \text {ns}\left (\left .\left (-\frac {1}{2}+\frac {i}{2}\right ) \sqrt [4]{c_1} \left (x+c_2\right )\right |-1\right ){}^2\right \},\left \{y(x)\to -\frac {1}{2} i \sqrt {c_1} \text {ns}\left (\left .\left (-\frac {1}{2}+\frac {i}{2}\right ) \sqrt [4]{c_1} \left (x+c_2\right )\right |-1\right ){}^2\right \}\right \}\]
Maple ✓
cpu = 0.072 (sec), leaf count = 53
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{\it \_C1}\,{\it \_a}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{\it \_C1}\,{\it \_a}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[2*y[x]*y''[x] == 8*y[x]^3 + y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (-I/2)*Sqrt[C[1]]*JacobiNS[(-1/2 + I/2)*C[1]^(1/4)*(x + C[2]), -1]^2}, {y[x] -> (-I/2)*Sqrt[C[1]]*JacobiNS[(-1/2 + I/2)*C[1]^(1/4)*(x + C[2]), -1]^2}}
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = 8*y(x)^3+diff(y(x),x)^2, y(x),'implicit')
Maple raw output
Intat(1/(4*_a^3+_C1*_a)^(1/2),_a = y(x))-x-_C2 = 0, Intat(-1/(4*_a^3+_C1*_a)^(1/2),_a = y(x))-x-_C2 = 0