75.13.2 problem 319

Internal problem ID [16907]
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 13. Basic concepts and definitions. Exercises page 98
Problem number : 319
Date solved : Tuesday, January 28, 2025 at 09:40:35 AM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} x y^{\prime \prime \prime }&=2 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(x*diff(y(x),x$3)=2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[x*D[y[x],{x,3}]==2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \log (x)+\left (-\frac {3}{2}+c_3\right ) x^2+c_2 x+c_1 \]