ODE
\[ y''(x) y'''(x)=2 \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0255832 (sec), leaf count = 61
\[\left \{\left \{y(x)\to -\frac {1}{15} \sqrt {2} \left (c_1+2 x\right ){}^{5/2}+c_3 x+c_2\right \},\left \{y(x)\to \frac {1}{15} \sqrt {2} \left (c_1+2 x\right ){}^{5/2}+c_3 x+c_2\right \}\right \}\]
Maple ✓
cpu = 0.105 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) =-{\frac {8}{15} \left ( {\it \_C1}+x \right ) ^{{\frac {5}{2}}}}+{\it \_C2}\,x+{\it \_C3},y \left ( x \right ) ={\frac {8}{15} \left ( {\it \_C1}+x \right ) ^{{\frac {5}{2}}}}+{\it \_C2}\,x+{\it \_C3} \right \} \] Mathematica raw input
DSolve[y''[x]*y'''[x] == 2,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[2]*(2*x + C[1])^(5/2))/15 + C[2] + x*C[3]}, {y[x] -> (Sqrt[2]*(2*x + C[1])^(5/2))/15 + C[2] + x*C[3]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)*diff(diff(diff(y(x),x),x),x) = 2, y(x),'implicit')
Maple raw output
y(x) = -8/15*(_C1+x)^(5/2)+_C2*x+_C3, y(x) = 8/15*(_C1+x)^(5/2)+_C2*x+_C3