ODE
\[ -x^3-(1-3 x) x y'(x)+y'(x)^3+(1-3 x) y'(x)^2-1=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Use new variable
Mathematica ✗
cpu = 599.997 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.225 (sec), leaf count = 378
\[ \left \{ y \left ( x \right ) =\int \!{-i \left ( \left ( -{\frac {i}{12}}-{\frac {\sqrt {3}}{12}} \right ) \left ( 36\,x+100+12\,\sqrt {3}\sqrt {4\,{x}^{3}-{x}^{2}+18\,x+23} \right ) ^{{\frac {2}{3}}}+ \left ( x-{\frac {1}{3}} \right ) \left ( i\sqrt [3]{36\,x+100+12\,\sqrt {3}\sqrt {4\,{x}^{3}-{x}^{2}+18\,x+23}}+i-\sqrt {3} \right ) \right ) {\frac {1}{\sqrt [3]{36\,x+100+12\,\sqrt {3}\sqrt {4\,{x}^{3}-{x}^{2}+18\,x+23}}}}}\,{\rm d}x+{\it \_C1},y \left ( x \right ) =\int \!{-i \left ( \left ( -{\frac {i}{12}}+{\frac {\sqrt {3}}{12}} \right ) \left ( 36\,x+100+12\,\sqrt {3}\sqrt {4\,{x}^{3}-{x}^{2}+18\,x+23} \right ) ^{{\frac {2}{3}}}+ \left ( i\sqrt [3]{36\,x+100+12\,\sqrt {3}\sqrt {4\,{x}^{3}-{x}^{2}+18\,x+23}}+i+\sqrt {3} \right ) \left ( x-{\frac {1}{3}} \right ) \right ) {\frac {1}{\sqrt [3]{36\,x+100+12\,\sqrt {3}\sqrt {4\,{x}^{3}-{x}^{2}+18\,x+23}}}}}\,{\rm d}x+{\it \_C1},y \left ( x \right ) =\int \!{\frac {1}{6} \left ( \left ( 6\,\sqrt [3]{36\,x+100+12\,\sqrt {3}\sqrt {4\,{x}^{3}-{x}^{2}+18\,x+23}}-12 \right ) x+ \left ( 36\,x+100+12\,\sqrt {3}\sqrt {4\,{x}^{3}-{x}^{2}+18\,x+23} \right ) ^{{\frac {2}{3}}}-2\,\sqrt [3]{36\,x+100+12\,\sqrt {3}\sqrt {4\,{x}^{3}-{x}^{2}+18\,x+23}}+4 \right ) {\frac {1}{\sqrt [3]{36\,x+100+12\,\sqrt {3}\sqrt {4\,{x}^{3}-{x}^{2}+18\,x+23}}}}}\,{\rm d}x+{\it \_C1} \right \} \] Mathematica raw input
DSolve[-1 - x^3 - (1 - 3*x)*x*y'[x] + (1 - 3*x)*y'[x]^2 + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3+(1-3*x)*diff(y(x),x)^2-x*(1-3*x)*diff(y(x),x)-1-x^3 = 0, y(x),'implicit')
Maple raw output
y(x) = Int(-I/(36*x+100+12*3^(1/2)*(4*x^3-x^2+18*x+23)^(1/2))^(1/3)*((-1/12*I+1/12*3^(1/2))*(36*x+100+12*3^(1/2)*(4*x^3-x^2+18*x+23)^(1/2))^(2/3)+(I*(36*x+100+12*3^(1/2)*(4*x^3-x^2+18*x+23)^(1/2))^(1/3)+I+3^(1/2))*(x-1/3)),x)+_C1, y(x) = Int(-I*((-1/12*I-1/12*3^(1/2))*(36*x+100+12*3^(1/2)*(4*x^3-x^2+18*x+23)^(1/2))^(2/3)+(x-1/3)*(I*(36*x+100+12*3^(1/2)*(4*x^3-x^2+18*x+23)^(1/2))^(1/3)+I-3^(1/2)))/(36*x+100+12*3^(1/2)*(4*x^3-x^2+18*x+23)^(1/2))^(1/3),x)+_C1, y(x) = Int(1/6*((6*(36*x+100+12*3^(1/2)*(4*x^3-x^2+18*x+23)^(1/2))^(1/3)-12)*x+(36*x+100+12*3^(1/2)*(4*x^3-x^2+18*x+23)^(1/2))^(2/3)-2*(36*x+100+12*3^(1/2)*(4*x^3-x^2+18*x+23)^(1/2))^(1/3)+4)/(36*x+100+12*3^(1/2)*(4*x^3-x^2+18*x+23)^(1/2))^(1/3),x)+_C1