75.13.2 problem 319

Internal problem ID [16836]
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 : Monday, March 31, 2025 at 03:23:51 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=x*diff(diff(diff(y(x),x),x),x) = 2; 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.189 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 3)) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + x^{2} \log {\left (x \right )} \]