Internal problem ID [9045]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1466.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y-{\mathrm e}^{a x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 36
dsolve(diff(diff(diff(y(x),x),x),x)-3*a*diff(diff(y(x),x),x)+3*a^2*diff(y(x),x)-a^3*y(x)-exp(a*x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3} {\mathrm e}^{a x}}{6}+c_{1} {\mathrm e}^{a x}+c_{2} {\mathrm e}^{a x} x +c_{3} {\mathrm e}^{a x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 34
DSolve[-E^(a*x) - a^3*y[x] + 3*a^2*y'[x] - 3*a*y''[x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{a x} \left (x^3+6 c_3 x^2+6 c_2 x+6 c_1\right ) \\ \end{align*}