Internal problem ID [13525]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 47.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }+8 y={\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve(diff(y(x),x$3)+8*y(x)=exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \,{\mathrm e}^{-2 x}}{12}+c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{x} \cos \left (\sqrt {3}\, x \right )+c_{3} {\mathrm e}^{x} \sin \left (\sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.337 (sec). Leaf size: 57
DSolve[y'''[x]+8*y[x]==Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{24} e^{-2 x} \left (2 x+24 c_3 e^{3 x} \cos \left (\sqrt {3} x\right )+24 c_2 e^{3 x} \sin \left (\sqrt {3} x\right )+1+24 c_1\right ) \]