23.1.259 problem 253

Internal problem ID [4866]
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 : 253
Date solved : Tuesday, September 30, 2025 at 08:45:41 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);
 

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 32

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}{2 x}-b-\frac {3 c x}{2}+c x \log (x)+c_1 x \end{align*}

✓ Sympy. Time used: 0.150 (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)
 

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