Internal problem ID [5964]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 69
Problem number: 1(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 i y^{\prime }+y=x} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+2*I*diff(y(x),x)+y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-i x} \sin \left (\sqrt {2}\, x \right ) c_{2} +{\mathrm e}^{-i x} \cos \left (\sqrt {2}\, x \right ) c_{1} +x -2 i \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 44
DSolve[y''[x]+2*I*y'[x]+y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x+c_1 e^{-i \left (1+\sqrt {2}\right ) x}+c_2 e^{i \left (\sqrt {2}-1\right ) x}-2 i \]