Internal problem ID [5211]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 i y^{\prime }+y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+2*I*diff(y(x),x)+y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-i x} \sin \left (x \sqrt {2}\right ) c_{2}+{\mathrm e}^{-i x} \cos \left (x \sqrt {2}\right ) c_{1}-2 i+x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 43
DSolve[y''[x]+2*I*y'[x]+y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+e^{-i \left (1+\sqrt {2}\right ) x} \left (c_2 e^{2 i \sqrt {2} x}+c_1\right )-2 i \\ \end{align*}