Internal problem ID [5226]
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).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 i y^{\prime \prime }-3 y^{\prime }+i y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
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)
\[ y \relax (x ) = c_{1} {\mathrm e}^{i x}+c_{2} {\mathrm e}^{i x} x +c_{3} {\mathrm e}^{i x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 25
DSolve[y'''[x]-3*I*y''[x]-3*y'[x]+I*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{i x} (x (c_3 x+c_2)+c_1) \\ \end{align*}