23.1.260 problem 254

Internal problem ID [4867]
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 : 254
Date solved : Tuesday, September 30, 2025 at 08:45:42 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

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

\[ y = \frac {x c}{2}+b +\frac {a \ln \left (x \right )}{x}+\frac {c_1}{x} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to \frac {a \log (x)}{x}+b+\frac {c x}{2}+\frac {c_1}{x} \end{align*}

✓ Sympy. Time used: 0.149 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \frac {C_{1}}{x} + \frac {a \log {\left (x \right )}}{x} + b + \frac {c x}{2} \]