Internal problem ID [5673]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of
First-Order Differential Equations Page 162
Problem number: 5 solved directly.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-x +y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 11
dsolve([diff(y(x),x)=x-y(x),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = x -1+{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 13
DSolve[{y'[x]==x-y[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+e^{-x}-1 \\ \end{align*}