81.12.1 problem 16-1

Internal problem ID [21654]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 16. Variation of Parameters. Page 375.
Problem number : 16-1
Date solved : Thursday, October 02, 2025 at 07:59:29 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {4 y}{x}&=x^{4} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(y(x),x)+4*y(x)/x = x^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{9}+9 c_1}{9 x^{4}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 19

ode=D[y[x],x]+4/x*y[x]==x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^5}{9}+\frac {c_1}{x^4} \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 + Derivative(y(x), x) + 4*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{9}}{9}}{x^{4}} \]