ODE
\[ y'''(x)=a y''(x) \] ODE Classification
[[_3rd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.172296 (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 = 0.012 (sec), leaf count = 15
\[[y \left (x \right ) = \textit {\_C1} +\textit {\_C2} x +\textit {\_C3} \,{\mathrm e}^{a x}]\] 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))
Maple raw output
[y(x) = _C1+_C2*x+_C3*exp(a*x)]