83.28.4 problem 4

Internal problem ID [19298]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (B) at page 106
Problem number : 4
Date solved : Monday, March 31, 2025 at 07:06:00 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} x^{3} y^{\prime \prime \prime }&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=x^3*diff(diff(diff(y(x),x),x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=x^3*D[y[x],{x,3}]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\log (x)}{2}+x (c_3 x+c_2)+c_1 \]

✓ Sympy. Time used: 0.275 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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