ODE
\[ \text {a0} y'(x)^2+\text {a1} y'(x)+\text {a2}+\text {a3} y(x)+y'(x)^3=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✗
cpu = 600.03 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.158 (sec), leaf count = 831
\[ \left \{ x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{36\,{\it a1}\,{\it a0}-108\,{\it a3}\,{\it \_a}-108\,{\it a2}-8\,{{\it a0}}^{3}+12\,\sqrt { \left ( 12\,{\it a3}\,{\it \_a}+12\,{\it a2} \right ) {{\it a0}}^{3}-3\,{{\it a1}}^{2}{{\it a0}}^{2}-54\,{\it a1}\, \left ( {\it a3}\,{\it \_a}+{\it a2} \right ) {\it a0}+81\,{{\it \_a}}^{2}{{\it a3}}^{2}+162\,{\it \_a}\,{\it a2}\,{\it a3}+12\,{{\it a1}}^{3}+81\,{{\it a2}}^{2}}}}{ \left ( 36\,{\it a1}\,{\it a0}-108\,{\it a3}\,{\it \_a}-108\,{\it a2}-8\,{{\it a0}}^{3}+12\,\sqrt { \left ( 12\,{\it a3}\,{\it \_a}+12\,{\it a2} \right ) {{\it a0}}^{3}-3\,{{\it a1}}^{2}{{\it a0}}^{2}-54\,{\it a1}\, \left ( {\it a3}\,{\it \_a}+{\it a2} \right ) {\it a0}+81\,{{\it \_a}}^{2}{{\it a3}}^{2}+162\,{\it \_a}\,{\it a2}\,{\it a3}+12\,{{\it a1}}^{3}+81\,{{\it a2}}^{2}} \right ) ^{2/3}-2\,{\it a0}\,\sqrt [3]{36\,{\it a1}\,{\it a0}-108\,{\it a3}\,{\it \_a}-108\,{\it a2}-8\,{{\it a0}}^{3}+12\,\sqrt { \left ( 12\,{\it a3}\,{\it \_a}+12\,{\it a2} \right ) {{\it a0}}^{3}-3\,{{\it a1}}^{2}{{\it a0}}^{2}-54\,{\it a1}\, \left ( {\it a3}\,{\it \_a}+{\it a2} \right ) {\it a0}+81\,{{\it \_a}}^{2}{{\it a3}}^{2}+162\,{\it \_a}\,{\it a2}\,{\it a3}+12\,{{\it a1}}^{3}+81\,{{\it a2}}^{2}}}+4\,{{\it a0}}^{2}-12\,{\it a1}}}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{36\,{\it a1}\,{\it a0}-108\,{\it a3}\,{\it \_a}-108\,{\it a2}-8\,{{\it a0}}^{3}+12\,\sqrt { \left ( 12\,{\it a3}\,{\it \_a}+12\,{\it a2} \right ) {{\it a0}}^{3}-3\,{{\it a1}}^{2}{{\it a0}}^{2}-54\,{\it a1}\, \left ( {\it a3}\,{\it \_a}+{\it a2} \right ) {\it a0}+81\,{{\it \_a}}^{2}{{\it a3}}^{2}+162\,{\it \_a}\,{\it a2}\,{\it a3}+12\,{{\it a1}}^{3}+81\,{{\it a2}}^{2}}}}{ \left ( i\sqrt {3}-1 \right ) \left ( 1/2\, \left ( 36\,{\it a1}\,{\it a0}-108\,{\it a3}\,{\it \_a}-108\,{\it a2}-8\,{{\it a0}}^{3}+12\,\sqrt { \left ( 12\,{\it a3}\,{\it \_a}+12\,{\it a2} \right ) {{\it a0}}^{3}-3\,{{\it a1}}^{2}{{\it a0}}^{2}-54\,{\it a1}\, \left ( {\it a3}\,{\it \_a}+{\it a2} \right ) {\it a0}+81\,{{\it \_a}}^{2}{{\it a3}}^{2}+162\,{\it \_a}\,{\it a2}\,{\it a3}+12\,{{\it a1}}^{3}+81\,{{\it a2}}^{2}} \right ) ^{2/3}+1/2\,{\it a0}\, \left ( i\sqrt {3}+1 \right ) \sqrt [3]{36\,{\it a1}\,{\it a0}-108\,{\it a3}\,{\it \_a}-108\,{\it a2}-8\,{{\it a0}}^{3}+12\,\sqrt { \left ( 12\,{\it a3}\,{\it \_a}+12\,{\it a2} \right ) {{\it a0}}^{3}-3\,{{\it a1}}^{2}{{\it a0}}^{2}-54\,{\it a1}\, \left ( {\it a3}\,{\it \_a}+{\it a2} \right ) {\it a0}+81\,{{\it \_a}}^{2}{{\it a3}}^{2}+162\,{\it \_a}\,{\it a2}\,{\it a3}+12\,{{\it a1}}^{3}+81\,{{\it a2}}^{2}}}+ \left ( {{\it a0}}^{2}-3\,{\it a1} \right ) \left ( i\sqrt {3}-1 \right ) \right ) }}{d{\it \_a}}-{\it \_C1}=0,x-\int ^{y \left ( x \right ) }\!6\,{\frac {\sqrt [3]{36\,{\it a1}\,{\it a0}-108\,{\it a3}\,{\it \_a}-108\,{\it a2}-8\,{{\it a0}}^{3}+12\,\sqrt { \left ( 12\,{\it a3}\,{\it \_a}+12\,{\it a2} \right ) {{\it a0}}^{3}-3\,{{\it a1}}^{2}{{\it a0}}^{2}-54\,{\it a1}\, \left ( {\it a3}\,{\it \_a}+{\it a2} \right ) {\it a0}+81\,{{\it \_a}}^{2}{{\it a3}}^{2}+162\,{\it \_a}\,{\it a2}\,{\it a3}+12\,{{\it a1}}^{3}+81\,{{\it a2}}^{2}}}}{ \left ( -1/2\, \left ( 36\,{\it a1}\,{\it a0}-108\,{\it a3}\,{\it \_a}-108\,{\it a2}-8\,{{\it a0}}^{3}+12\,\sqrt { \left ( 12\,{\it a3}\,{\it \_a}+12\,{\it a2} \right ) {{\it a0}}^{3}-3\,{{\it a1}}^{2}{{\it a0}}^{2}-54\,{\it a1}\, \left ( {\it a3}\,{\it \_a}+{\it a2} \right ) {\it a0}+81\,{{\it \_a}}^{2}{{\it a3}}^{2}+162\,{\it \_a}\,{\it a2}\,{\it a3}+12\,{{\it a1}}^{3}+81\,{{\it a2}}^{2}} \right ) ^{2/3}+1/2\, \left ( i\sqrt {3}-1 \right ) {\it a0}\,\sqrt [3]{36\,{\it a1}\,{\it a0}-108\,{\it a3}\,{\it \_a}-108\,{\it a2}-8\,{{\it a0}}^{3}+12\,\sqrt { \left ( 12\,{\it a3}\,{\it \_a}+12\,{\it a2} \right ) {{\it a0}}^{3}-3\,{{\it a1}}^{2}{{\it a0}}^{2}-54\,{\it a1}\, \left ( {\it a3}\,{\it \_a}+{\it a2} \right ) {\it a0}+81\,{{\it \_a}}^{2}{{\it a3}}^{2}+162\,{\it \_a}\,{\it a2}\,{\it a3}+12\,{{\it a1}}^{3}+81\,{{\it a2}}^{2}}}+ \left ( {{\it a0}}^{2}-3\,{\it a1} \right ) \left ( i\sqrt {3}+1 \right ) \right ) \left ( i\sqrt {3}+1 \right ) }}{d{\it \_a}}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[a2 + a3*y[x] + a1*y'[x] + a0*y'[x]^2 + y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(diff(y(x),x)^3+a0*diff(y(x),x)^2+a1*diff(y(x),x)+a2+a3*y(x) = 0, y(x),'implicit')
Maple raw output
x-Intat(6/((36*a1*a0-108*a3*_a-108*a2-8*a0^3+12*((12*_a*a3+12*a2)*a0^3-3*a1^2*a0^2-54*a1*(_a*a3+a2)*a0+81*_a^2*a3^2+162*_a*a2*a3+12*a1^3+81*a2^2)^(1/2))^(2/3)-2*a0*(36*a1*a0-108*a3*_a-108*a2-8*a0^3+12*((12*_a*a3+12*a2)*a0^3-3*a1^2*a0^2-54*a1*(_a*a3+a2)*a0+81*_a^2*a3^2+162*_a*a2*a3+12*a1^3+81*a2^2)^(1/2))^(1/3)+4*a0^2-12*a1)*(36*a1*a0-108*a3*_a-108*a2-8*a0^3+12*((12*_a*a3+12*a2)*a0^3-3*a1^2*a0^2-54*a1*(_a*a3+a2)*a0+81*_a^2*a3^2+162*_a*a2*a3+12*a1^3+81*a2^2)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(6*(36*a1*a0-108*a3*_a-108*a2-8*a0^3+12*((12*_a*a3+12*a2)*a0^3-3*a1^2*a0^2-54*a1*(_a*a3+a2)*a0+81*_a^2*a3^2+162*_a*a2*a3+12*a1^3+81*a2^2)^(1/2))^(1/3)/(-1/2*(36*a1*a0-108*a3*_a-108*a2-8*a0^3+12*((12*_a*a3+12*a2)*a0^3-3*a1^2*a0^2-54*a1*(_a*a3+a2)*a0+81*_a^2*a3^2+162*_a*a2*a3+12*a1^3+81*a2^2)^(1/2))^(2/3)+1/2*(I*3^(1/2)-1)*a0*(36*a1*a0-108*a3*_a-108*a2-8*a0^3+12*((12*_a*a3+12*a2)*a0^3-3*a1^2*a0^2-54*a1*(_a*a3+a2)*a0+81*_a^2*a3^2+162*_a*a2*a3+12*a1^3+81*a2^2)^(1/2))^(1/3)+(a0^2-3*a1)*(I*3^(1/2)+1))/(I*3^(1/2)+1),_a = y(x))-_C1 = 0, x-Intat(6*(36*a1*a0-108*a3*_a-108*a2-8*a0^3+12*((12*_a*a3+12*a2)*a0^3-3*a1^2*a0^2-54*a1*(_a*a3+a2)*a0+81*_a^2*a3^2+162*_a*a2*a3+12*a1^3+81*a2^2)^(1/2))^(1/3)/(I*3^(1/2)-1)/(1/2*(36*a1*a0-108*a3*_a-108*a2-8*a0^3+12*((12*_a*a3+12*a2)*a0^3-3*a1^2*a0^2-54*a1*(_a*a3+a2)*a0+81*_a^2*a3^2+162*_a*a2*a3+12*a1^3+81*a2^2)^(1/2))^(2/3)+1/2*a0*(I*3^(1/2)+1)*(36*a1*a0-108*a3*_a-108*a2-8*a0^3+12*((12*_a*a3+12*a2)*a0^3-3*a1^2*a0^2-54*a1*(_a*a3+a2)*a0+81*_a^2*a3^2+162*_a*a2*a3+12*a1^3+81*a2^2)^(1/2))^(1/3)+(a0^2-3*a1)*(I*3^(1/2)-1)),_a = y(x))-_C1 = 0