75.14.10 problem 336

Internal problem ID [16924]
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 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 336
Date solved : Tuesday, January 28, 2025 at 09:41:02 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x \ln \left (x \right ) y^{\prime \prime }&=y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve(x*ln(x)*diff(y(x),x$2)=diff(y(x),x),y(x), singsol=all)
 

\[ y = c_{1} +x \left (-1+\ln \left (x \right )\right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 19

DSolve[x*Log[x]*D[y[x],{x,2}]==D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 (-x)+c_1 x \log (x)+c_2 \]