ODE
\[ y'''(x)=a^2 y(x) \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.153799 (sec), leaf count = 53
\[\left \{\left \{y(x)\to c_1 e^{(-1)^{2/3} a^{2/3} x}+c_2 e^{-\sqrt [3]{-1} a^{2/3} x}+c_3 e^{a^{2/3} x}\right \}\right \}\]
Maple ✓
cpu = 0.022 (sec), leaf count = 53
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{\left (-\frac {a^{\frac {2}{3}}}{2}-\frac {i \sqrt {3}\, a^{\frac {2}{3}}}{2}\right ) x}+\textit {\_C2} \,{\mathrm e}^{\left (-\frac {a^{\frac {2}{3}}}{2}+\frac {i \sqrt {3}\, a^{\frac {2}{3}}}{2}\right ) x}+\textit {\_C3} \,{\mathrm e}^{a^{\frac {2}{3}} x}\right ]\] Mathematica raw input
DSolve[y'''[x] == a^2*y[x],y[x],x]
Mathematica raw output
{{y[x] -> E^((-1)^(2/3)*a^(2/3)*x)*C[1] + C[2]/E^((-1)^(1/3)*a^(2/3)*x) + E^(a^(2/3)*x)*C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x) = a^2*y(x), y(x))
Maple raw output
[y(x) = _C1*exp((-1/2*a^(2/3)-1/2*I*3^(1/2)*a^(2/3))*x)+_C2*exp((-1/2*a^(2/3)+1/2*I*3^(1/2)*a^(2/3))*x)+_C3*exp(a^(2/3)*x)]