49.4.7 problem 1(g)

Internal problem ID [7618]
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(g)
Date solved : Monday, January 27, 2025 at 03:07:44 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)+(3*I-1)*diff(y(x),x)-3*I*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-3 i x}+{\mathrm e}^{x} c_{2} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]+(3*I-1)*D[y[x],x]-3*I*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{-3 i x}+c_2 e^x \]