Internal problem ID [15408]
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: 639.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 12
dsolve([x^2*(ln(x)-1)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,x],singsol=all)
\[ y \left (x \right ) = c_{1} x +c_{2} \ln \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 16
DSolve[x^2*(Log[x]-1)*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x-c_2 \log (x) \]