Internal problem ID [5222]
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).
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 }+4 y^{\prime }-4 i y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
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)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-2 i x}+c_{2} {\mathrm e}^{i x}+c_{3} {\mathrm e}^{2 i x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 36
DSolve[y'''[x]-I*y''[x]+4*y'[x]-4*I*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 i x} \left (c_2 e^{4 i x}+c_3 e^{3 i x}+c_1\right ) \\ \end{align*}