Internal problem ID [4357]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \ln \relax (y) y^{\prime }-\ln \relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (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 \relax (x ) = {\mathrm e}^{\sqrt {\ln \relax (x )^{2}+2 c_{1}}} \\ y \relax (x ) = {\mathrm e}^{-\sqrt {\ln \relax (x )^{2}+2 c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.745 (sec). Leaf size: 60
DSolve[x*Log[y[x]]*y'[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*}