35.2.5 problem 5

Internal problem ID [6097]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 2. Separable equations. page 398
Problem number : 5
Date solved : Monday, January 27, 2025 at 01:36:01 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 8

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

\[ y = x +\ln \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 9

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

\[ y(x)\to x+\log (x) \]