Internal problem ID [5950]
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(g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x$2)+(3*I-1)*diff(y(x),x)-3*I*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{-3 i x} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 22
DSolve[y''[x]+(3*I-1)*y'[x]-3*I*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-3 i x}+c_2 e^x \]