35.8.2 problem 2

Internal problem ID [6209]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 2
Date solved : Monday, January 27, 2025 at 01:47:45 PM
CAS classification : [_separable]

\begin{align*} x \ln \left (y\right ) y^{\prime }-y \ln \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 31

dsolve(x*ln(y(x))*diff(y(x),x)-y(x)*ln(x)=0,y(x), singsol=all)
 

\begin{align*} y &= {\mathrm e}^{\sqrt {\ln \left (x \right )^{2}+2 c_{1}}} \\ y &= {\mathrm e}^{-\sqrt {\ln \left (x \right )^{2}+2 c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.786 (sec). Leaf size: 60

DSolve[x*Log[y[x]]*D[y[x],x]-y[x]*Log[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{-\sqrt {\log ^2(x)+2 c_1}} \\ y(x)\to e^{\sqrt {\log ^2(x)+2 c_1}} \\ y(x)\to 0 \\ y(x)\to e^{2 i \text {Interval}[\{0,\pi \}]} \\ \end{align*}