Internal problem ID [2964]
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]
Solve \begin {gather*} \boxed {y^{\prime } x -\left (1+\ln \relax (x )-\ln \relax (y)\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(x*diff(y(x),x) = (1+ln(x)-ln(y(x)))*y(x),y(x), singsol=all)
\[ y \relax (x ) = x \,{\mathrm e}^{-\frac {c_{1}}{x}} \]
✓ Solution by Mathematica
Time used: 0.203 (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*}