Internal problem ID [15194]
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 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 336.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x*ln(x)*diff(y(x),x$2)=diff(y(x),x),y(x), singsol=all)
\[ y = \ln \left (x \right ) c_{2} x -c_{2} x +c_{1} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 19
DSolve[x*Log[x]*y''[x]==y'[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 (-x)+c_1 x \log (x)+c_2 \]