Internal problem ID [5235]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 83
Problem number: 3(a).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-i y^{\prime \prime }+y^{\prime }-i y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 27
dsolve(diff(y(x),x$3)-I*diff(y(x),x$2)+diff(y(x),x)-I*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-i x} c_{1}+c_{2} {\mathrm e}^{i x}+c_{3} {\mathrm e}^{i x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[y'''[x]-I*y''[x]+y'[x]-I*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-i x} \left (e^{2 i x} (c_3 x+c_2)+c_1\right ) \\ \end{align*}