35.9.2 problem 1, using elementary method

Internal problem ID [6237]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 1, using elementary method
Date solved : Monday, January 27, 2025 at 01:49:45 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 9

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

\[ y = {\mathrm e}^{x} x c_{1} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 17

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

\begin{align*} y(x)\to c_1 e^x x \\ y(x)\to 0 \\ \end{align*}