29.6.13 problem 159

Internal problem ID [4759]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 159
Date solved : Sunday, March 30, 2025 at 03:53:06 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: 0.051 (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: 0.256 (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)
 

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