29.15.8 problem 416

Internal problem ID [5014]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 416
Date solved : Monday, January 27, 2025 at 10:03:37 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (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: 0.042 (sec). Leaf size: 16

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

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