77.1.8 problem 19 (page 30)

Internal problem ID [17898]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 19 (page 30)
Date solved : Tuesday, January 28, 2025 at 11:10:57 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 11

dsolve(diff(y(x),x)=y(x)/x*(1+ln(y(x))-ln(x)),y(x), singsol=all)
 

\[ y = x \,{\mathrm e}^{-c_{1} x} \]

✓ Solution by Mathematica

Time used: 0.196 (sec). Leaf size: 20

DSolve[D[y[x],x]==y[x]/x*(1+Log[y[x]]-Log[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x e^{e^{c_1} x} \\ y(x)\to x \\ \end{align*}