32.6.27 problem Exercise 12.27, page 103

Internal problem ID [5892]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.27, page 103
Date solved : Sunday, March 30, 2025 at 10:24:07 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+a y+b \,x^{n}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=x*diff(y(x),x)+a*y(x)+b*x^n = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 25

ode=x*D[y[x],x]+a*y[x]+b*x^n==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.326 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = \frac {\left (C_{1} \left (a + n\right ) - b e^{\left (a + n\right ) \log {\left (x \right )}}\right ) e^{- a \log {\left (x \right )}}}{a + n} \]