Internal problem ID [5992]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 89
Problem number: 1(b).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-8 y={\mathrm e}^{i x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(diff(y(x),x$3)-8*y(x)=exp(I*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-\frac {8}{65}+\frac {i}{65}\right ) {\mathrm e}^{i x}+{\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right )+c_{3} {\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.472 (sec). Leaf size: 59
DSolve[y'''[x]-8*y[x]==Exp[I*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{65} e^{-x} \left (-(8-i) e^{(1+i) x}+65 c_1 e^{3 x}+65 c_2 \cos \left (\sqrt {3} x\right )+65 c_3 \sin \left (\sqrt {3} x\right )\right ) \]