Internal problem ID [8529]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 193.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x y^{\prime } \ln \left (x \right )+y=a x \left (1+\ln \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(x*diff(y(x),x)*ln(x) + y(x) - a*x*(ln(x)+1)=0,y(x), singsol=all)
\[ y \left (x \right ) = a x +\frac {c_{1}}{\ln \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 16
DSolve[x*y'[x]*Log[x] + y[x] - a*x*(Log[x]+1)==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to a x+\frac {c_1}{\log (x)} \]