29.9.10 problem 250

Internal problem ID [4850]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 250
Date solved : Tuesday, March 04, 2025 at 07:22:50 PM
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);
 

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

✓ Mathematica. Time used: 0.061 (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]
 

\[ y(x)\to -\frac {a}{2 x}-b-\frac {3 c x}{2}+c x \log (x)+c_1 x \]

✓ Sympy. Time used: 0.234 (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)
 

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