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 = 1.88752 (sec), leaf count = 131
\[\left \{\left \{y(x)\to c_3-\frac {c_1 \left (c_2+x\right ) \sqrt {c_1^2 x^2+2 c_2 c_1^2 x+c_2^2 c_1^2+1}+\sinh ^{-1}\left (c_1 \left (c_2+x\right )\right )}{2 c_1^{3/2}}\right \},\left \{y(x)\to \frac {c_1 \left (c_2+x\right ) \sqrt {c_1^2 x^2+2 c_2 c_1^2 x+c_2^2 c_1^2+1}+\sinh ^{-1}\left (c_1 \left (c_2+x\right )\right )}{2 c_1^{3/2}}+c_3\right \}\right \}\]
Maple ✓
cpu = 0.166 (sec), leaf count = 151
\[ \left \{ y \left ( x \right ) =-{\frac {1}{2\,{\it \_C1}} \left ( \ln \left ( \sqrt {{\it \_C1}\, \left ( 1+ \left ( x+{\it \_C2} \right ) ^{2}{{\it \_C1}}^{2} \right ) }+{ \left ( x+{\it \_C2} \right ) {{\it \_C1}}^{3}{\frac {1}{\sqrt {{{\it \_C1}}^{3}}}}} \right ) {\it \_C1}+\sqrt {{{\it \_C1}}^{3}} \left ( \left ( x+{\it \_C2} \right ) \sqrt {{\it \_C1}\, \left ( 1+ \left ( x+{\it \_C2} \right ) ^{2}{{\it \_C1}}^{2} \right ) }-2\,{\it \_C1}\,{\it \_C3} \right ) \right ) {\frac {1}{\sqrt {{{\it \_C1}}^{3}}}}},y \left ( x \right ) ={\frac {1}{2\,{\it \_C1}} \left ( \ln \left ( \sqrt {{\it \_C1}\, \left ( 1+ \left ( x+{\it \_C2} \right ) ^{2}{{\it \_C1}}^{2} \right ) }+{ \left ( x+{\it \_C2} \right ) {{\it \_C1}}^{3}{\frac {1}{\sqrt {{{\it \_C1}}^{3}}}}} \right ) {\it \_C1}+\sqrt {{{\it \_C1}}^{3}} \left ( \left ( x+{\it \_C2} \right ) \sqrt {{\it \_C1}\, \left ( 1+ \left ( x+{\it \_C2} \right ) ^{2}{{\it \_C1}}^{2} \right ) }+2\,{\it \_C1}\,{\it \_C3} \right ) \right ) {\frac {1}{\sqrt {{{\it \_C1}}^{3}}}}} \right \} \] Mathematica raw input
DSolve[y'[x]^3*y'''[x] == 1,y[x],x]
Mathematica raw output
{{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]}, {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),'implicit')
Maple raw output
y(x) = 1/2/(_C1^3)^(1/2)*(ln((_C1*(1+(x+_C2)^2*_C1^2))^(1/2)+(x+_C2)*_C1^3/(_C1^3)^(1/2))*_C1+(_C1^3)^(1/2)*((x+_C2)*(_C1*(1+(x+_C2)^2*_C1^2))^(1/2)+2*_C1*_C3))/_C1, y(x) = -1/2/(_C1^3)^(1/2)*(ln((_C1*(1+(x+_C2)^2*_C1^2))^(1/2)+(x+_C2)*_C1^3/(_C1^3)^(1/2))*_C1+(_C1^3)^(1/2)*((x+_C2)*(_C1*(1+(x+_C2)^2*_C1^2))^(1/2)-2*_C1*_C3))/_C1