Internal problem ID [5014]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x}{y}-\frac {y}{x}=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.265 (sec). Leaf size: 34
dsolve([diff(y(x),x)=x/y(x)+y(x)/x,y(-1) = 0],y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {2 \ln \relax (x )-2 i \pi }\, x \\ y \relax (x ) = -\sqrt {2 \ln \relax (x )-2 i \pi }\, x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.277 (sec). Leaf size: 48
DSolve[{y'[x]==x/y[x]+y[x]/x,{y[-1]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} x \sqrt {\log (x)-i \pi } \\ y(x)\to \sqrt {2} x \sqrt {\log (x)-i \pi } \\ \end{align*}