ODE
\[ y'''(x)+a y(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.155594 (sec), leaf count = 54
\[\left \{\left \{y(x)\to c_1 e^{-(-1)^{2/3} \sqrt [3]{a} x}+c_2 e^{\sqrt [3]{-1} \sqrt [3]{a} x}+c_3 e^{-\sqrt [3]{a} x}\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 63
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\left (-\frac {\left (-a \right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (-a \right )^{\frac {1}{3}}}{2}\right ) x}+\textit {\_C2} \,{\mathrm e}^{\left (-\frac {\left (-a \right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (-a \right )^{\frac {1}{3}}}{2}\right ) x}+\textit {\_C3} \,{\mathrm e}^{\left (-a \right )^{\frac {1}{3}} x}\right ]\] Mathematica raw input
DSolve[a*y[x] + y'''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^((-1)^(2/3)*a^(1/3)*x) + E^((-1)^(1/3)*a^(1/3)*x)*C[2] + C[3]/E^(a^(1/3)*x)}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x)+a*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp((-1/2*(-a)^(1/3)+1/2*I*3^(1/2)*(-a)^(1/3))*x)+_C2*exp((-1/2*(-a)^(1/3)-1/2*I*3^(1/2)*(-a)^(1/3))*x)+_C3*exp((-a)^(1/3)*x)]