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 = 600.034 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.362 (sec), leaf count = 1027
\[\left [x -\left (\int _{}^{y \left (x \right )}\frac {6 \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}}{\left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {2}{3}}-2 \mathit {a0} \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}+4 \mathit {a0}^{2}-12 \mathit {a1}}d \textit {\_a} \right )-\textit {\_C1} = 0, x -\left (\int _{}^{y \left (x \right )}\frac {12 \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}}{\left (1+i \sqrt {3}\right ) \left (i \sqrt {3}\, \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}} \mathit {a0} +2 i \sqrt {3}\, \mathit {a0}^{2}-6 i \sqrt {3}\, \mathit {a1} -\left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {2}{3}}-\mathit {a0} \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}+2 \mathit {a0}^{2}-6 \mathit {a1} \right )}d \textit {\_a} \right )-\textit {\_C1} = 0, x -\left (\int _{}^{y \left (x \right )}\frac {12 \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}}{\left (-1+i \sqrt {3}\right ) \left (i \sqrt {3}\, \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}} \mathit {a0} +2 i \sqrt {3}\, \mathit {a0}^{2}-6 i \sqrt {3}\, \mathit {a1} +\left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {2}{3}}+\mathit {a0} \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a2} -108 \mathit {a3} \textit {\_a} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}-2 \mathit {a0}^{2}+6 \mathit {a1} \right )}d \textit {\_a} \right )-\textit {\_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))
Maple raw output
[x-Intat(6/((36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(2/3)-2*a0*(36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(1/3)+4*a0^2-12*a1)*(36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(12/(1+I*3^(1/2))/(I*3^(1/2)*(36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(1/3)*a0+2*I*3^(1/2)*a0^2-6*I*3^(1/2)*a1-(36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(2/3)-a0*(36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(1/3)+2*a0^2-6*a1)*(36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(12/(-1+I*3^(1/2))/(I*3^(1/2)*(36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(1/3)*a0+2*I*3^(1/2)*a0^2-6*I*3^(1/2)*a1+(36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(2/3)+a0*(36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(1/3)-2*a0^2+6*a1)*(36*a1*a0-108*a2-108*a3*_a-8*a0^3+12*(12*_a*a0^3*a3+81*_a^2*a3^2-54*_a*a0*a1*a3+12*a0^3*a2-3*a0^2*a1^2+162*_a*a2*a3-54*a0*a1*a2+12*a1^3+81*a2^2)^(1/2))^(1/3),_a = y(x))-_C1 = 0]