23.1.162 problem 162

Internal problem ID [4769]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 162
Date solved : Tuesday, September 30, 2025 at 08:30:59 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+\left (b x +a \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = c_1 \,{\mathrm e}^{-b x} x^{-a} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to c_1 x^{-a} e^{-a-b x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.158 (sec). Leaf size: 15

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

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