23.1.263 problem 257

Internal problem ID [4870]
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 : 257
Date solved : Tuesday, September 30, 2025 at 08:45:48 AM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime }&=\left (b x +a \right ) y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=x^2*diff(y(x),x) = (b*x+a)*y(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 28

ode=x^2*D[y[x],x]==(a+b*x)*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.212 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) - (a + b*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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