63.1.44 problem 63

Internal problem ID [15484]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 63
Date solved : Thursday, October 02, 2025 at 10:18:27 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {n y}{x}&=a \,x^{-n} \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 15

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

\[ y = \left (a x +c_1 \right ) x^{-n} \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to x^{-n} (a x+c_1) \end{align*}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded