60.2.69 problem 645

Internal problem ID [10656]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 645
Date solved : Monday, January 27, 2025 at 09:22:07 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.067 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.275 (sec). Leaf size: 20

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

\[ y(x)\to e^{x-e^{-x+c_1}-1} \]