Internal problem ID [5175]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 1.6 Introduction– Linear equations of First Order. Page 41
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+i y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 17
dsolve(diff(y(x),x)+I*y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = -i x +1+{\mathrm e}^{-i x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 22
DSolve[y'[x]+I*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i x+c_1 e^{-i x}+1 \\ \end{align*}