ODE
\[ y'(x)^3-2 y(x) y'(x)+y(x)^2=0 \] 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 = 0.052 (sec), leaf count = 259
\[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}}}}{ \left ( -108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}} \right ) ^{2/3}+24\,{\it \_a}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!12\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}}}}{ \left ( i\sqrt {3}-1 \right ) \left ( 12\,i{\it \_a}\,\sqrt {3}+ \left ( -108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}} \right ) ^{2/3}-12\,{\it \_a} \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!12\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}}}}{ \left ( i\sqrt {3}+1 \right ) \left ( 12\,i{\it \_a}\,\sqrt {3}- \left ( -108\,{{\it \_a}}^{2}+12\,\sqrt {3}\sqrt {27\,{{\it \_a}}^{4}-32\,{{\it \_a}}^{3}} \right ) ^{2/3}+12\,{\it \_a} \right ) }}{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y[x]^2 - 2*y[x]*y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
""
Maple raw input
dsolve(diff(y(x),x)^3-2*y(x)*diff(y(x),x)+y(x)^2 = 0, y(x),'implicit')
Maple raw output
x-Intat(6/((-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(2/3)+24*_a)*(-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(12/(I*3^(1/2)+1)/(12*I*_a*3^(1/2)-(-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(2/3)+12*_a)*(-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(12/(I*3^(1/2)-1)/(12*I*_a*3^(1/2)+(-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(2/3)-12*_a)*(-108*_a^2+12*3^(1/2)*(27*_a^4-32*_a^3)^(1/2))^(1/3),_a = y(x))-_C1 = 0