49.2.6 problem 2

Internal problem ID [7596]
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
Date solved : Monday, January 27, 2025 at 03:07:01 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+i y&=x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(diff(y(x),x)+I*y(x)=x,y(x), singsol=all)
 

\[ y = -i x +1+{\mathrm e}^{-i x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 22

DSolve[D[y[x],x]+I*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -i x+c_1 e^{-i x}+1 \]