67.2.47 problem Problem 18(L)

Internal problem ID [14004]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 18(L)
Date solved : Tuesday, January 28, 2025 at 06:11:36 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x}&=1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(x*ln(x)*diff(y(x),x$2)+2*diff(y(x),x)-y(x)/x=1,y(x), singsol=all)
 

\[ y = \frac {c_{1}}{\ln \left (x \right )}+x +\frac {c_{2} x}{\ln \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 23

DSolve[x*Log[x]*D[y[x],{x,2}]+2*D[y[x],x]-y[x]/x==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x \log (x)+(-1+c_2) x+c_1}{\log (x)} \]