ODE
\[ y'''(x)=a y''(x) \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0156643 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {c_1 e^{a x}}{a^2}+c_3 x+c_2\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\it \_C2}\,x+{\it \_C3}\,{{\rm e}^{ax}} \right \} \] Mathematica raw input
DSolve[y'''[x] == a*y''[x],y[x],x]
Mathematica raw output
{{y[x] -> (E^(a*x)*C[1])/a^2 + C[2] + x*C[3]}}
Maple raw input
dsolve(diff(diff(diff(y(x),x),x),x) = a*diff(diff(y(x),x),x), y(x),'implicit')
Maple raw output
y(x) = _C1+_C2*x+_C3*exp(a*x)