8.2.6 problem 6

Internal problem ID [666]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 6
Date solved : Monday, January 27, 2025 at 02:56:57 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=1+x -y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

dsolve(diff(y(x),x) = 1+x-y(x),y(x), singsol=all)
 

\[ y = x +{\mathrm e}^{-x} c_1 \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 15

DSolve[D[y[x],x] == 1+x-y[x],y[x],x,IncludeSingularSolutions -> True]
 

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