75.14.5 problem 331

Internal problem ID [16919]
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 : 331
Date solved : Tuesday, January 28, 2025 at 09:40:54 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

\[ y = -\frac {5 x^{3}}{18}+\frac {x^{3} \ln \left (x \right )}{3}+c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 28

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

\[ y(x)\to -\frac {5 x^3}{18}+\frac {1}{3} x^3 \log (x)+c_2 x+c_1 \]