Internal problem ID [9054]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1475.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 y^{\prime \prime \prime }-8 y^{\prime \prime }-11 y^{\prime }-3 y+18 \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 26
dsolve(4*diff(diff(diff(y(x),x),x),x)-8*diff(diff(y(x),x),x)-11*diff(y(x),x)-3*y(x)+18*exp(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x}+c_{1} {\mathrm e}^{3 x}+c_{2} {\mathrm e}^{-\frac {x}{2}}+c_{3} {\mathrm e}^{-\frac {x}{2}} x \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 32
DSolve[18*E^x - 3*y[x] - 11*y'[x] - 8*y''[x] + 4*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x+e^{-x/2} (c_2 x+c_1)+c_3 e^{3 x} \\ \end{align*}