49.7.8 problem 4(i)

Internal problem ID [7647]
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(i)
Date solved : Monday, January 27, 2025 at 03:08:57 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 25

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

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