4.6.1 problem 1

Internal problem ID [1218]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 04:29:51 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {x^{3}-2 y}{x} \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 16

ode:=diff(y(x),x) = (x^3-2*y(x))/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{5}+5 c_1}{5 x^{2}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \frac {x^3}{5}+\frac {c_1}{x^2} \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{5}}{5}}{x^{2}} \]