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 = 2.49055 (sec), leaf count = 62
\[\left \{\left \{y(x)\to -\frac {\sqrt {a^2+c_1^2 \left (c_2+x\right ){}^2}}{\sqrt {c_1}}\right \},\left \{y(x)\to \frac {\sqrt {a^2+c_1^2 \left (c_2+x\right ){}^2}}{\sqrt {c_1}}\right \}\right \}\]
Maple ✓
cpu = 2.174 (sec), leaf count = 56
\[ \left \{ -{\frac {1}{{\it \_C1}}\sqrt {{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2}}}-x-{\it \_C2}=0,{\frac {1}{{\it \_C1}}\sqrt {{\it \_C1}\, \left ( y \left ( x \right ) \right ) ^{2}-{a}^{2}}}-x-{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
-1/_C1*(_C1*y(x)^2-a^2)^(1/2)-x-_C2 = 0, 1/_C1*(_C1*y(x)^2-a^2)^(1/2)-x-_C2 = 0