ODE
\[ y'(x)^3+y'(x)^2-y(x)=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✗
cpu = 0 (sec), leaf count = 0 , crash
Kernel Crash
Maple ✓
cpu = 0.103 (sec), leaf count = 436
\[ \left \{ x-\int ^{y \left ( x \right ) }\!3\,{\frac {\sqrt [3]{6}\sqrt [3]{\sqrt {3} \left ( 27\,\sqrt {3}{\it \_a}-2\,\sqrt {3}+9\,\sqrt {27\,{{\it \_a}}^{2}-4\,{\it \_a}} \right ) }}{{6}^{2/3}-\sqrt [3]{6}\sqrt [3]{\sqrt {3} \left ( 27\,\sqrt {3}{\it \_a}-2\,\sqrt {3}+9\,\sqrt {27\,{{\it \_a}}^{2}-4\,{\it \_a}} \right ) }+ \left ( \sqrt {3} \left ( 27\,\sqrt {3}{\it \_a}-2\,\sqrt {3}+9\,\sqrt {27\,{{\it \_a}}^{2}-4\,{\it \_a}} \right ) \right ) ^{2/3}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{3}\sqrt [3]{2}\sqrt [3]{\sqrt {3} \left ( 27\,\sqrt {3}{\it \_a}-2\,\sqrt {3}+9\,\sqrt {27\,{{\it \_a}}^{2}-4\,{\it \_a}} \right ) }}{ \left ( i\sqrt {3}-1 \right ) \left ( \sqrt [3]{3}\sqrt [3]{2}+\sqrt [3]{\sqrt {3} \left ( 27\,\sqrt {3}{\it \_a}-2\,\sqrt {3}+9\,\sqrt {27\,{{\it \_a}}^{2}-4\,{\it \_a}} \right ) } \right ) \left ( \left ( i/2{3}^{5/6}-1/2\,\sqrt [3]{3} \right ) \sqrt [3]{2}+\sqrt [3]{\sqrt {3} \left ( 27\,\sqrt {3}{\it \_a}-2\,\sqrt {3}+9\,\sqrt {27\,{{\it \_a}}^{2}-4\,{\it \_a}} \right ) } \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!12\,{\frac {\sqrt [3]{3}\sqrt [3]{2}\sqrt [3]{\sqrt {3} \left ( 27\,\sqrt {3}{\it \_a}-2\,\sqrt {3}+9\,\sqrt {27\,{{\it \_a}}^{2}-4\,{\it \_a}} \right ) }}{ \left ( i\sqrt {3}+1 \right ) \left ( \sqrt [3]{3}\sqrt [3]{2}+\sqrt [3]{\sqrt {3} \left ( 27\,\sqrt {3}{\it \_a}-2\,\sqrt {3}+9\,\sqrt {27\,{{\it \_a}}^{2}-4\,{\it \_a}} \right ) } \right ) \left ( -2\,\sqrt [3]{\sqrt {3} \left ( 27\,\sqrt {3}{\it \_a}-2\,\sqrt {3}+9\,\sqrt {27\,{{\it \_a}}^{2}-4\,{\it \_a}} \right ) }+ \left ( i{3}^{5/6}+\sqrt [3]{3} \right ) \sqrt [3]{2} \right ) }}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[-y[x] + y'[x]^2 + y'[x]^3 == 0,y[x],x]
Mathematica raw output
""
Maple raw input
dsolve(diff(y(x),x)^3+diff(y(x),x)^2-y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = 0, x-Intat(3*6^(1/3)/(6^(2/3)-6^(1/3)*(3^(1/2)*(27*3^(1/2)*_a-2*3^(1/2)+9*(27*_a^2-4*_a)^(1/2)))^(1/3)+(3^(1/2)*(27*3^(1/2)*_a-2*3^(1/2)+9*(27*_a^2-4*_a)^(1/2)))^(2/3))*(3^(1/2)*(27*3^(1/2)*_a-2*3^(1/2)+9*(27*_a^2-4*_a)^(1/2)))^(1/3),_a = y(x))-_C1 = 0, x-Intat(12*3^(1/3)*2^(1/3)*(3^(1/2)*(27*3^(1/2)*_a-2*3^(1/2)+9*(27*_a^2-4*_a)^(1/2)))^(1/3)/(I*3^(1/2)+1)/(3^(1/3)*2^(1/3)+(3^(1/2)*(27*3^(1/2)*_a-2*3^(1/2)+9*(27*_a^2-4*_a)^(1/2)))^(1/3))/(-2*(3^(1/2)*(27*3^(1/2)*_a-2*3^(1/2)+9*(27*_a^2-4*_a)^(1/2)))^(1/3)+(I*3^(5/6)+3^(1/3))*2^(1/3)),_a = y(x))-_C1 = 0, x-Intat(6*3^(1/3)*2^(1/3)*(3^(1/2)*(27*3^(1/2)*_a-2*3^(1/2)+9*(27*_a^2-4*_a)^(1/2)))^(1/3)/(I*3^(1/2)-1)/(3^(1/3)*2^(1/3)+(3^(1/2)*(27*3^(1/2)*_a-2*3^(1/2)+9*(27*_a^2-4*_a)^(1/2)))^(1/3))/((1/2*I*3^(5/6)-1/2*3^(1/3))*2^(1/3)+(3^(1/2)*(27*3^(1/2)*_a-2*3^(1/2)+9*(27*_a^2-4*_a)^(1/2)))^(1/3)),_a = y(x))-_C1 = 0