49.7.4 problem 4(d)

Internal problem ID [7643]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 74
Problem number : 4(d)
Date solved : Monday, January 27, 2025 at 03:08:55 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-i y^{\prime \prime }+4 y^{\prime }-4 i y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(diff(y(x),x$3)-I*diff(y(x),x$2)+4*diff(y(x),x)-4*I*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-2 i x}+c_{2} {\mathrm e}^{2 i x}+c_3 \,{\mathrm e}^{i x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 36

DSolve[D[y[x],{x,3}]-I*D[y[x],{x,2}]+4*D[y[x],x]-4*I*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 i x} \left (c_2 e^{4 i x}+c_3 e^{3 i x}+c_1\right ) \]