Internal problem ID [3472]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 216.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {x y^{\prime }-\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve(x*diff(y(x),x) = (1+ln(x)-ln(y(x)))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = x \,{\mathrm e}^{\frac {c_{1}}{x}} \]
✓ Solution by Mathematica
Time used: 0.196 (sec). Leaf size: 22
DSolve[x y'[x]==(1+Log[x]-Log[y[x]])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x e^{\frac {e^{c_1}}{x}} y(x)\to x \end{align*}