25.1.16 problem 16

Internal problem ID [4228]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 16
Date solved : Monday, January 27, 2025 at 08:43:05 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 10

dsolve([x*diff(y(x),x)=x*y(x)+y(x),y(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 12

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

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