49.9.8 problem 3(b)

Internal problem ID [7657]
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(b)
Date solved : Monday, January 27, 2025 at 03:09:06 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 i y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

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

\[ y(x)\to e^{i x} (c_2 x+c_1) \]