80.4.1 problem 1

Internal problem ID [18552]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 31. Problems at page 85
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 11:58:07 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

\[ y \left (x \right ) = 1+{\mathrm e}^{-\frac {x^{2}}{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 24

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

\begin{align*} y(x)\to 1+c_1 e^{-\frac {x^2}{2}} \\ y(x)\to 1 \\ \end{align*}