47.2.19 problem 19

Internal problem ID [7435]
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
Date solved : Monday, January 27, 2025 at 02:57:36 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.065 (sec). Leaf size: 32

dsolve([diff(y(x),x)=x/y(x)+y(x)/x,y(-1) = 0],y(x), singsol=all)
 

\begin{align*} y &= \sqrt {2 \ln \left (x \right )-2 i \pi }\, x \\ y &= -\sqrt {2 \ln \left (x \right )-2 i \pi }\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.184 (sec). Leaf size: 48

DSolve[{D[y[x],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*}