Internal problem ID [9793]
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]]
\[ \boxed {y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y={\mathrm e}^{x a}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
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)
\[ y \left (x \right ) = {\mathrm e}^{a x} \left (\frac {1}{6} x^{3}+c_{1} +x c_{2} +x^{2} c_{3} \right ) \]
✓ 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]
\[ y(x)\to \frac {1}{6} e^{a x} \left (x^3+6 c_3 x^2+6 c_2 x+6 c_1\right ) \]