89.5.24 problem 24

Internal problem ID [24374]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 24
Date solved : Thursday, October 02, 2025 at 10:22:33 PM
CAS classification : [_linear]

\begin{align*} \left (x +a \right ) y^{\prime }&=b x -n y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 31

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

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

✓ Mathematica. Time used: 0.555 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {b (n x-a)}{n (n+1)}+c_1 (a+x)^{-n} \end{align*}

✓ Sympy. Time used: 7.326 (sec). Leaf size: 442

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

\[ \text {Solution too large to show} \]