ODE
\[ y(x)^3 y''(x)=a^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 1.6816 (sec), leaf count = 62
\[\left \{\left \{y(x)\to -\frac {\sqrt {a^2+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}}\right \},\left \{y(x)\to \frac {\sqrt {a^2+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}}\right \}\right \}\]
Maple ✓
cpu = 2.333 (sec), leaf count = 74
\[\left [y \left (x \right ) = \frac {\sqrt {\textit {\_C1} \left (\textit {\_C1}^{2} \textit {\_C2}^{2}+2 \textit {\_C1}^{2} \textit {\_C2} x +\textit {\_C1}^{2} x^{2}+a^{2}\right )}}{\textit {\_C1}}, y \left (x \right ) = -\frac {\sqrt {\textit {\_C1} \left (\textit {\_C1}^{2} \textit {\_C2}^{2}+2 \textit {\_C1}^{2} \textit {\_C2} x +\textit {\_C1}^{2} x^{2}+a^{2}\right )}}{\textit {\_C1}}\right ]\] Mathematica raw input
DSolve[y[x]^3*y''[x] == a^2,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[a^2 + C[1]^2*(x + C[2])^2]/Sqrt[C[1]])}, {y[x] -> Sqrt[a^2 + C[1]^2*(x + C[2])^2]/Sqrt[C[1]]}}
Maple raw input
dsolve(y(x)^3*diff(diff(y(x),x),x) = a^2, y(x))
Maple raw output
[y(x) = 1/_C1*(_C1*(_C1^2*_C2^2+2*_C1^2*_C2*x+_C1^2*x^2+a^2))^(1/2), y(x) = -1/_C1*(_C1*(_C1^2*_C2^2+2*_C1^2*_C2*x+_C1^2*x^2+a^2))^(1/2)]