75.20.34 problem 673

Internal problem ID [17168]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 673
Date solved : Tuesday, January 28, 2025 at 09:55:56 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+y x&=2 \ln \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.160 (sec). Leaf size: 16

dsolve([x^3*(ln(x)-1)*diff(y(x),x$2)-x^2*diff(y(x),x)+x*y(x)=2*ln(x),y(infinity) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 8

DSolve[{x^3*(Log[x]-1)*D[y[x],{x,2}]-x^2*D[y[x],x]+x*y[x]==2*Log[x],{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{x} \]