Internal problem ID [15189]
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: 331.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime }=2 \ln \left (x \right ) x} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.006 (sec). Leaf size: 28
DSolve[y''[x]==2*x*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {5 x^3}{18}+\frac {1}{3} x^3 \log (x)+c_2 x+c_1 \]