Internal problem ID [15009]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 102.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _dAlembert]
\[ \boxed {y^{\prime } x -y \left (\ln \left (y\right )-\ln \left (x \right )\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve(x*diff(y(x),x)=y(x)*( ln(y(x))-ln(x) ),y(x), singsol=all)
\[ y = {\mathrm e}^{c_{1} x +1} x \]
✓ Solution by Mathematica
Time used: 0.226 (sec). Leaf size: 24
DSolve[x*y'[x]==y[x]*( Log[y[x]]-Log[x] ),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x e^{1+e^{c_1} x} \\ y(x)\to e x \\ \end{align*}