49.10.2 problem 1(b)

Internal problem ID [7660]
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)
Date solved : Monday, January 27, 2025 at 03:09:08 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-8 y&={\mathrm e}^{i x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 41

dsolve(diff(y(x),x$3)-8*y(x)=exp(I*x),y(x), singsol=all)
 

\[ y = \left (-\frac {8}{65}+\frac {i}{65}\right ) {\mathrm e}^{i x}+{\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right )+c_3 \,{\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right ) \]

✓ Solution by Mathematica

Time used: 0.424 (sec). Leaf size: 59

DSolve[D[y[x],{x,3}]-8*y[x]==Exp[I*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{65} e^{-x} \left (-(8-i) e^{(1+i) x}+65 c_1 e^{3 x}+65 c_2 \cos \left (\sqrt {3} x\right )+65 c_3 \sin \left (\sqrt {3} x\right )\right ) \]