81.3.3 problem 3

Internal problem ID [18621]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 12:04:24 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 13

dsolve(diff(y(x),x)=x-y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = x -1+{\mathrm e}^{-x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 16

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

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