69.1.74 problem 118

Internal problem ID [14148]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 118
Date solved : Wednesday, March 05, 2025 at 10:36:49 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.006 (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: 0.186 (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)
 

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