Internal problem ID [15438]
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 ODE’s). Section 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 673.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+y x=2 \ln \left (x \right )} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (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)
\[ y \left (x \right ) = \frac {-c_{1} \ln \left (x \right ) x +1}{x} \]
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 8
DSolve[{x^3*(Log[x]-1)*y''[x]-x^2*y'[x]+x*y[x]==2*Log[x],{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{x} \]