ODE
\[ y'''(x)=a^2 y(x) \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00904729 (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 = 0.01 (sec), leaf count = 47
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-{\frac { \left ( i\sqrt {3}+1 \right ) x}{2}{a}^{{\frac {2}{3}}}}}}+{\it \_C2}\,{{\rm e}^{{\frac { \left ( i\sqrt {3}-1 \right ) x}{2}{a}^{{\frac {2}{3}}}}}}+{\it \_C3}\,{{\rm e}^{{a}^{{\frac {2}{3}}}x}} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*exp(-1/2*a^(2/3)*(I*3^(1/2)+1)*x)+_C2*exp(1/2*a^(2/3)*(I*3^(1/2)-1)*x)+_C3*exp(a^(2/3)*x)