ODE
\[ y'(x)^3 y'''(x)=1 \] ODE Classification
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]]
Book solution method
TO DO
Mathematica ✓
cpu = 1.71957 (sec), leaf count = 131
\[\left \{\left \{y(x)\to c_3-\frac {c_1 (x+c_2) \sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x+1+c_2{}^2 c_1{}^2}+\sinh ^{-1}(c_1 (x+c_2))}{2 c_1{}^{3/2}}\right \},\left \{y(x)\to \frac {c_1 (x+c_2) \sqrt {c_1{}^2 x^2+2 c_2 c_1{}^2 x+1+c_2{}^2 c_1{}^2}+\sinh ^{-1}(c_1 (x+c_2))}{2 c_1{}^{3/2}}+c_3\right \}\right \}\]
Maple ✓
cpu = 2.908 (sec), leaf count = 249
\[\left [y \left (x \right ) = \frac {\sqrt {\textit {\_C1} \left (\textit {\_C1}^{2} \textit {\_C2}^{2}+2 \textit {\_C1}^{2} \textit {\_C2} x +\textit {\_C1}^{2} x^{2}+1\right )}\, x}{2 \textit {\_C1}}+\frac {\sqrt {\textit {\_C1} \left (\textit {\_C1}^{2} \textit {\_C2}^{2}+2 \textit {\_C1}^{2} \textit {\_C2} x +\textit {\_C1}^{2} x^{2}+1\right )}\, \textit {\_C2}}{2 \textit {\_C1}}+\frac {\ln \left (\frac {\textit {\_C1}^{3} \textit {\_C2} +\textit {\_C1}^{3} x}{\sqrt {\textit {\_C1}^{3}}}+\sqrt {\textit {\_C1} \left (\textit {\_C1}^{2} \textit {\_C2}^{2}+2 \textit {\_C1}^{2} \textit {\_C2} x +\textit {\_C1}^{2} x^{2}+1\right )}\right )}{2 \sqrt {\textit {\_C1}^{3}}}+\textit {\_C3}, y \left (x \right ) = -\frac {\sqrt {\textit {\_C1} \left (\textit {\_C1}^{2} \textit {\_C2}^{2}+2 \textit {\_C1}^{2} \textit {\_C2} x +\textit {\_C1}^{2} x^{2}+1\right )}\, x}{2 \textit {\_C1}}-\frac {\sqrt {\textit {\_C1} \left (\textit {\_C1}^{2} \textit {\_C2}^{2}+2 \textit {\_C1}^{2} \textit {\_C2} x +\textit {\_C1}^{2} x^{2}+1\right )}\, \textit {\_C2}}{2 \textit {\_C1}}-\frac {\ln \left (\frac {\textit {\_C1}^{3} \textit {\_C2} +\textit {\_C1}^{3} x}{\sqrt {\textit {\_C1}^{3}}}+\sqrt {\textit {\_C1} \left (\textit {\_C1}^{2} \textit {\_C2}^{2}+2 \textit {\_C1}^{2} \textit {\_C2} x +\textit {\_C1}^{2} x^{2}+1\right )}\right )}{2 \sqrt {\textit {\_C1}^{3}}}+\textit {\_C3}\right ]\] Mathematica raw input
DSolve[y'[x]^3*y'''[x] == 1,y[x],x]
Mathematica raw output
{{y[x] -> -1/2*(ArcSinh[C[1]*(x + C[2])] + C[1]*(x + C[2])*Sqrt[1 + x^2*C[1]^2 + 2*x*C[1]^2*C[2] + C[1]^2*C[2]^2])/C[1]^(3/2) + C[3]}, {y[x] -> (ArcSinh[C[1]*(x + C[2])] + C[1]*(x + C[2])*Sqrt[1 + x^2*C[1]^2 + 2*x*C[1]^2*C[2] + C[1]^2*C[2]^2])/(2*C[1]^(3/2)) + C[3]}}
Maple raw input
dsolve(diff(y(x),x)^3*diff(diff(diff(y(x),x),x),x) = 1, y(x))
Maple raw output
[y(x) = 1/2/_C1*(_C1*(_C1^2*_C2^2+2*_C1^2*_C2*x+_C1^2*x^2+1))^(1/2)*x+1/2/_C1*(_C1*(_C1^2*_C2^2+2*_C1^2*_C2*x+_C1^2*x^2+1))^(1/2)*_C2+1/2*ln((_C1^3*_C2+_C1^3*x)/(_C1^3)^(1/2)+(_C1*(_C1^2*_C2^2+2*_C1^2*_C2*x+_C1^2*x^2+1))^(1/2))/(_C1^3)^(1/2)+_C3, y(x) = -1/2/_C1*(_C1*(_C1^2*_C2^2+2*_C1^2*_C2*x+_C1^2*x^2+1))^(1/2)*x-1/2/_C1*(_C1*(_C1^2*_C2^2+2*_C1^2*_C2*x+_C1^2*x^2+1))^(1/2)*_C2-1/2*ln((_C1^3*_C2+_C1^3*x)/(_C1^3)^(1/2)+(_C1*(_C1^2*_C2^2+2*_C1^2*_C2*x+_C1^2*x^2+1))^(1/2))/(_C1^3)^(1/2)+_C3]