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 = 0.194001 (sec), leaf count = 61
\[\left \{\left \{y(x)\to -\frac {1}{15} \sqrt {2} (2 x+c_1){}^{5/2}+c_3 x+c_2\right \},\left \{y(x)\to \frac {1}{15} \sqrt {2} (2 x+c_1){}^{5/2}+c_3 x+c_2\right \}\right \}\]
Maple ✓
cpu = 0.517 (sec), leaf count = 31
\[\left [y \left (x \right ) = -\frac {8 \left (x +\textit {\_C1} \right )^{\frac {5}{2}}}{15}+\textit {\_C2} x +\textit {\_C3}, y \left (x \right ) = \frac {8 \left (x +\textit {\_C1} \right )^{\frac {5}{2}}}{15}+\textit {\_C2} x +\textit {\_C3}\right ]\] Mathematica raw input
DSolve[y''[x]*y'''[x] == 2,y[x],x]
Mathematica raw output
{{y[x] -> -1/15*(Sqrt[2]*(2*x + C[1])^(5/2)) + 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))
Maple raw output
[y(x) = -8/15*(x+_C1)^(5/2)+_C2*x+_C3, y(x) = 8/15*(x+_C1)^(5/2)+_C2*x+_C3]