ODE
\[ y'''(x)+a y(x)=0 \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00774462 (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 = 0.01 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{{\frac { \left ( i\sqrt {3}-1 \right ) x}{2}\sqrt [3]{-a}}}}+{\it \_C2}\,{{\rm e}^{-{\frac { \left ( i\sqrt {3}+1 \right ) x}{2}\sqrt [3]{-a}}}}+{\it \_C3}\,{{\rm e}^{\sqrt [3]{-a}x}} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*exp(1/2*(-a)^(1/3)*(I*3^(1/2)-1)*x)+_C2*exp(-1/2*(-a)^(1/3)*(I*3^(1/2)+1)*x)+_C3*exp((-a)^(1/3)*x)