Internal problem ID [10920]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x}-1=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{1}}{\ln \left (x \right )}+x +\frac {c_{2} x}{\ln \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 21
DSolve[x*Log[x]*y''[x]+2*y'[x]-y[x]/x==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {(-1+c_2) x+c_1}{\log (x)} \\ \end{align*}