29.8.11 problem 216

Internal problem ID [4816]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 216
Date solved : Monday, January 27, 2025 at 09:41:07 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} x y^{\prime }&=\left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.029 (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: 0.202 (sec). Leaf size: 22

DSolve[x D[y[x],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*}