29.14.2 problem 381

Internal problem ID [4981]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 381
Date solved : Sunday, March 30, 2025 at 04:27:51 AM
CAS classification : [_linear]

\begin{align*} x^{n} y^{\prime }&=a +b \,x^{n -1} y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=x^n*diff(y(x),x) = a+b*x^(n-1)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {a \,x^{-n +1}}{n +b -1}+x^{b} c_1 \]

✓ Mathematica. Time used: 0.126 (sec). Leaf size: 28

ode=x^n D[y[x],x]==a+b x^(n-1) y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {a x^{1-n}}{b+n-1}+c_1 x^b \]

✗ Sympy

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

Timed Out