ODE
\[ y'''(x)+\text {a1} y''(x)+\text {a2} y'(x)+\text {a3} y(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.009094 (sec), leaf count = 84
\[\left \{\left \{y(x)\to c_1 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a1}+\text {$\#$1} \text {a2}+\text {a3}\& ,1\right ]}+c_2 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a1}+\text {$\#$1} \text {a2}+\text {a3}\& ,2\right ]}+c_3 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a1}+\text {$\#$1} \text {a2}+\text {a3}\& ,3\right ]}\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 542
\[ \left \{ y \left ( x \right ) ={\it \_C3}\,{{\rm e}^{{\frac {x}{6} \left ( \left ( 36\,{\it a2}\,{\it a1}-108\,{\it a3}-8\,{{\it a1}}^{3}+12\,\sqrt {81\,{{\it a3}}^{2}+ \left ( 12\,{{\it a1}}^{3}-54\,{\it a2}\,{\it a1} \right ) {\it a3}-3\,{{\it a2}}^{2}{{\it a1}}^{2}+12\,{{\it a2}}^{3}} \right ) ^{{\frac {2}{3}}}-2\,{\it a1}\,\sqrt [3]{36\,{\it a2}\,{\it a1}-108\,{\it a3}-8\,{{\it a1}}^{3}+12\,\sqrt {81\,{{\it a3}}^{2}+ \left ( 12\,{{\it a1}}^{3}-54\,{\it a2}\,{\it a1} \right ) {\it a3}-3\,{{\it a2}}^{2}{{\it a1}}^{2}+12\,{{\it a2}}^{3}}}+4\,{{\it a1}}^{2}-12\,{\it a2} \right ) {\frac {1}{\sqrt [3]{36\,{\it a2}\,{\it a1}-108\,{\it a3}-8\,{{\it a1}}^{3}+12\,\sqrt {81\,{{\it a3}}^{2}+ \left ( 12\,{{\it a1}}^{3}-54\,{\it a2}\,{\it a1} \right ) {\it a3}-3\,{{\it a2}}^{2}{{\it a1}}^{2}+12\,{{\it a2}}^{3}}}}}}}}+{\it \_C2}\,{{\rm e}^{-{\frac {x}{3} \left ( \left ( -{\frac {i}{4}}\sqrt {3}+{\frac {1}{4}} \right ) \left ( 36\,{\it a2}\,{\it a1}-108\,{\it a3}-8\,{{\it a1}}^{3}+12\,\sqrt {81\,{{\it a3}}^{2}+ \left ( 12\,{{\it a1}}^{3}-54\,{\it a2}\,{\it a1} \right ) {\it a3}-3\,{{\it a2}}^{2}{{\it a1}}^{2}+12\,{{\it a2}}^{3}} \right ) ^{{\frac {2}{3}}}+{\it a1}\,\sqrt [3]{36\,{\it a2}\,{\it a1}-108\,{\it a3}-8\,{{\it a1}}^{3}+12\,\sqrt {81\,{{\it a3}}^{2}+ \left ( 12\,{{\it a1}}^{3}-54\,{\it a2}\,{\it a1} \right ) {\it a3}-3\,{{\it a2}}^{2}{{\it a1}}^{2}+12\,{{\it a2}}^{3}}}+ \left ( {{\it a1}}^{2}-3\,{\it a2} \right ) \left ( i\sqrt {3}+1 \right ) \right ) {\frac {1}{\sqrt [3]{36\,{\it a2}\,{\it a1}-108\,{\it a3}-8\,{{\it a1}}^{3}+12\,\sqrt {81\,{{\it a3}}^{2}+ \left ( 12\,{{\it a1}}^{3}-54\,{\it a2}\,{\it a1} \right ) {\it a3}-3\,{{\it a2}}^{2}{{\it a1}}^{2}+12\,{{\it a2}}^{3}}}}}}}}+{\it \_C1}\,{{\rm e}^{{\frac {x}{3} \left ( \left ( -{\frac {i}{4}}\sqrt {3}-{\frac {1}{4}} \right ) \left ( 36\,{\it a2}\,{\it a1}-108\,{\it a3}-8\,{{\it a1}}^{3}+12\,\sqrt {81\,{{\it a3}}^{2}+ \left ( 12\,{{\it a1}}^{3}-54\,{\it a2}\,{\it a1} \right ) {\it a3}-3\,{{\it a2}}^{2}{{\it a1}}^{2}+12\,{{\it a2}}^{3}} \right ) ^{{\frac {2}{3}}}-{\it a1}\,\sqrt [3]{36\,{\it a2}\,{\it a1}-108\,{\it a3}-8\,{{\it a1}}^{3}+12\,\sqrt {81\,{{\it a3}}^{2}+ \left ( 12\,{{\it a1}}^{3}-54\,{\it a2}\,{\it a1} \right ) {\it a3}-3\,{{\it a2}}^{2}{{\it a1}}^{2}+12\,{{\it a2}}^{3}}}+ \left ( {{\it a1}}^{2}-3\,{\it a2} \right ) \left ( i\sqrt {3}-1 \right ) \right ) {\frac {1}{\sqrt [3]{36\,{\it a2}\,{\it a1}-108\,{\it a3}-8\,{{\it a1}}^{3}+12\,\sqrt {81\,{{\it a3}}^{2}+ \left ( 12\,{{\it a1}}^{3}-54\,{\it a2}\,{\it a1} \right ) {\it a3}-3\,{{\it a2}}^{2}{{\it a1}}^{2}+12\,{{\it a2}}^{3}}}}}}}} \right \} \] Mathematica raw input
DSolve[a3*y[x] + a2*y'[x] + a1*y''[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(x*Root[a3 + a2*#1 + a1*#1^2 + #1^3 & , 1])*C[1] + E^(x*Root[a3 + a2*#1 + a1*#1^2 + #1^3 & , 2])*C[2] + E^(x*Root[a3 + a2*#1 + a1*#1^2 + #1^3 & , 3])*C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)+a1*diff(diff(y(x),x),x)+a2*diff(y(x),x)+a3*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C3*exp(1/6*((36*a2*a1-108*a3-8*a1^3+12*(81*a3^2+(12*a1^3-54*a1*a2)*a3-3*a2^2*a1^2+12*a2^3)^(1/2))^(2/3)-2*a1*(36*a2*a1-108*a3-8*a1^3+12*(81*a3^2+(12*a1^3-54*a1*a2)*a3-3*a2^2*a1^2+12*a2^3)^(1/2))^(1/3)+4*a1^2-12*a2)/(36*a2*a1-108*a3-8*a1^3+12*(81*a3^2+(12*a1^3-54*a1*a2)*a3-3*a2^2*a1^2+12*a2^3)^(1/2))^(1/3)*x)+_C2*exp(-1/3*((-1/4*I*3^(1/2)+1/4)*(36*a2*a1-108*a3-8*a1^3+12*(81*a3^2+(12*a1^3-54*a1*a2)*a3-3*a2^2*a1^2+12*a2^3)^(1/2))^(2/3)+a1*(36*a2*a1-108*a3-8*a1^3+12*(81*a3^2+(12*a1^3-54*a1*a2)*a3-3*a2^2*a1^2+12*a2^3)^(1/2))^(1/3)+(a1^2-3*a2)*(I*3^(1/2)+1))*x/(36*a2*a1-108*a3-8*a1^3+12*(81*a3^2+(12*a1^3-54*a1*a2)*a3-3*a2^2*a1^2+12*a2^3)^(1/2))^(1/3))+_C1*exp(1/3*((-1/4*I*3^(1/2)-1/4)*(36*a2*a1-108*a3-8*a1^3+12*(81*a3^2+(12*a1^3-54*a1*a2)*a3-3*a2^2*a1^2+12*a2^3)^(1/2))^(2/3)-a1*(36*a2*a1-108*a3-8*a1^3+12*(81*a3^2+(12*a1^3-54*a1*a2)*a3-3*a2^2*a1^2+12*a2^3)^(1/2))^(1/3)+(a1^2-3*a2)*(I*3^(1/2)-1))*x/(36*a2*a1-108*a3-8*a1^3+12*(81*a3^2+(12*a1^3-54*a1*a2)*a3-3*a2^2*a1^2+12*a2^3)^(1/2))^(1/3))