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 = 0.162575 (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 = 0.137 (sec), leaf count = 644
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-\frac {\left (i \left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {2}{3}} \sqrt {3}-4 i \sqrt {3}\, \mathit {a1}^{2}+12 i \sqrt {3}\, \mathit {a2} +\left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {2}{3}}+4 \mathit {a1} \left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {1}{3}}+4 \mathit {a1}^{2}-12 \mathit {a2} \right ) x}{12 \left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {1}{3}}}}+\textit {\_C2} \,{\mathrm e}^{\frac {\left (i \left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {2}{3}} \sqrt {3}-4 i \sqrt {3}\, \mathit {a1}^{2}+12 i \sqrt {3}\, \mathit {a2} -\left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {2}{3}}-4 \mathit {a1} \left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {1}{3}}-4 \mathit {a1}^{2}+12 \mathit {a2} \right ) x}{12 \left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {1}{3}}}}+\textit {\_C3} \,{\mathrm e}^{\frac {\left (\left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {2}{3}}-2 \mathit {a1} \left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {1}{3}}+4 \mathit {a1}^{2}-12 \mathit {a2} \right ) x}{6 \left (36 \mathit {a1} \mathit {a2} -108 \mathit {a3} -8 \mathit {a1}^{3}+12 \sqrt {12 \mathit {a1}^{3} \mathit {a3} -3 \mathit {a1}^{2} \mathit {a2}^{2}-54 \mathit {a2} \mathit {a3} \mathit {a1} +12 \mathit {a2}^{3}+81 \mathit {a3}^{2}}\right )^{\frac {1}{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))
Maple raw output
[y(x) = _C1*exp(-1/12*(I*(36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(2/3)*3^(1/2)-4*I*3^(1/2)*a1^2+12*I*3^(1/2)*a2+(36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(2/3)+4*a1*(36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(1/3)+4*a1^2-12*a2)/(36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(1/3)*x)+_C2*exp(1/12*(I*(36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(2/3)*3^(1/2)-4*I*3^(1/2)*a1^2+12*I*3^(1/2)*a2-(36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(2/3)-4*a1*(36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(1/3)-4*a1^2+12*a2)/(36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(1/3)*x)+_C3*exp(1/6*((36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(2/3)-2*a1*(36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(1/3)+4*a1^2-12*a2)/(36*a1*a2-108*a3-8*a1^3+12*(12*a1^3*a3-3*a1^2*a2^2-54*a1*a2*a3+12*a2^3+81*a3^2)^(1/2))^(1/3)*x)]