49.9.7 problem 3(a)

Internal problem ID [7656]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 83
Problem number : 3(a)
Date solved : Monday, January 27, 2025 at 03:09:05 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)-I*diff(y(x),x$2)+diff(y(x),x)-I*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-i x} c_{1} +\left (c_3 x +c_{2} \right ) {\mathrm e}^{i x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 31

DSolve[D[y[x],{x,3}]-I*D[y[x],{x,2}]+D[y[x],x]-I*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-i x} \left (e^{2 i x} (c_3 x+c_2)+c_1\right ) \]