Internal problem ID [5195]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 52
Problem number: 1(e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 i y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)+2*I*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-i x} \sin \left (x \sqrt {2}\right )+c_{2} {\mathrm e}^{-i x} \cos \left (x \sqrt {2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 38
DSolve[y''[x]+2*I*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-i \left (1+\sqrt {2}\right ) x} \left (c_2 e^{2 i \sqrt {2} x}+c_1\right ) \\ \end{align*}