60.1.192 problem 193

Internal problem ID [10206]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 193
Date solved : Monday, January 27, 2025 at 06:38:22 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime } \ln \left (x \right )+y-a x \left (\ln \left (x \right )+1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(x*diff(y(x),x)*ln(x) + y(x) - a*x*(ln(x)+1)=0,y(x), singsol=all)
 

\[ y = a x +\frac {c_{1}}{\ln \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 16

DSolve[x*D[y[x],x]*Log[x] + y[x] - a*x*(Log[x]+1)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to a x+\frac {c_1}{\log (x)} \]