49.4.5 problem 1(e)

Internal problem ID [7616]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 52
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:07:41 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: 0.001 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 38

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

\[ y(x)\to e^{-i \left (1+\sqrt {2}\right ) x} \left (c_2 e^{2 i \sqrt {2} x}+c_1\right ) \]