23.1.262 problem 256

Internal problem ID [4869]
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 : 256
Date solved : Tuesday, September 30, 2025 at 08:45:46 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 22

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 -\frac {a}{b x+x}+c_1 x^b \end{align*}

✓ Sympy. Time used: 0.265 (sec). Leaf size: 22

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

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