Internal problem ID [3670]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 416.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } x \ln \left (x \right )+y=a x \left (\ln \left (x \right )+1\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)*x*ln(x) = a*x*(1+ln(x))-y(x),y(x), singsol=all)
\[ y \left (x \right ) = a x +\frac {c_{1}}{\ln \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 16
DSolve[y'[x] x Log[x]==a x(1+Log[x])-y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to a x+\frac {c_1}{\log (x)} \]