Internal problem ID [4245]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x y y^{\prime }-x y-y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 8
dsolve([x*y(x)*diff(y(x),x)-x*y(x)=y(x),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = x +\ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 9
DSolve[{x*y[x]*y'[x]-x*y[x]==y[x],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\log (x) \\ \end{align*}