76.24.13 problem 15

Internal problem ID [17741]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.2 (Basic Theory of First Order Linear Systems). Problems at page 398
Problem number : 15
Date solved : Monday, March 31, 2025 at 04:26:20 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x y^{\prime \prime \prime }-y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

ode:=x*diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_3 \,x^{3}+c_2 x +c_1 \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 21

ode=x*D[y[x],{x,3}]-D[y[x],{x,2}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {c_1 x^3}{6}+c_3 x+c_2 \]

✓ Sympy. Time used: 0.053 (sec). Leaf size: 12

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

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