ODE
\[ y'(x)^3-y(x) y'(x)^2+y(x)^2=0 \] 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 = 0.086 (sec), leaf count = 370
\[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}}{ \left ( -108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}} \right ) ^{2/3}+2\,{\it \_a}\,\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}+4\,{{\it \_a}}^{2}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!12\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}}{ \left ( i\sqrt {3}-1 \right ) \left ( \sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}-2\,{\it \_a} \right ) \left ( \sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}-i\sqrt {3}{\it \_a}+{\it \_a} \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!-12\,{\frac {\sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}}{ \left ( i\sqrt {3}+1 \right ) \left ( \sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}+i\sqrt {3}{\it \_a}+{\it \_a} \right ) \left ( \sqrt [3]{-108\,{{\it \_a}}^{2}+8\,{{\it \_a}}^{3}+12\,\sqrt {-12\,{{\it \_a}}^{5}+81\,{{\it \_a}}^{4}}}-2\,{\it \_a} \right ) }}{d{\it \_a}}-{\it \_C1}=0,y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[y[x]^2 - y[x]*y'[x]^2 + y'[x]^3 == 0,y[x],x]
Mathematica raw output
""
Maple raw input
dsolve(diff(y(x),x)^3-y(x)*diff(y(x),x)^2+y(x)^2 = 0, y(x),'implicit')
Maple raw output
y(x) = 0, x-Intat(6/((-108*_a^2+8*_a^3+12*(-12*_a^5+81*_a^4)^(1/2))^(2/3)+2*_a*(-108*_a^2+8*_a^3+12*(-12*_a^5+81*_a^4)^(1/2))^(1/3)+4*_a^2)*(-108*_a^2+8*_a^3+12*(-12*_a^5+81*_a^4)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(-12/(I*3^(1/2)+1)/((-108*_a^2+8*_a^3+12*(-12*_a^5+81*_a^4)^(1/2))^(1/3)+I*3^(1/2)*_a+_a)/((-108*_a^2+8*_a^3+12*(-12*_a^5+81*_a^4)^(1/2))^(1/3)-2*_a)*(-108*_a^2+8*_a^3+12*(-12*_a^5+81*_a^4)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(12/(I*3^(1/2)-1)/((-108*_a^2+8*_a^3+12*(-12*_a^5+81*_a^4)^(1/2))^(1/3)-2*_a)/((-108*_a^2+8*_a^3+12*(-12*_a^5+81*_a^4)^(1/2))^(1/3)-I*3^(1/2)*_a+_a)*(-108*_a^2+8*_a^3+12*(-12*_a^5+81*_a^4)^(1/2))^(1/3),_a = y(x))-_C1 = 0