Internal problem ID [9802]
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]]
\[ \boxed {4 y^{\prime \prime \prime }-8 y^{\prime \prime }-11 y^{\prime }-3 y=-18 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
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)
\[ y \left (x \right ) = \left (c_{3} x +c_{2} \right ) {\mathrm e}^{-\frac {x}{2}}+c_{1} {\mathrm e}^{3 x}+{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 37
DSolve[18*E^x - 3*y[x] - 11*y'[x] - 8*y''[x] + 4*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/2} \left (e^{3 x/2}+c_2 x+c_3 e^{7 x/2}+c_1\right ) \]