23.1.335 problem 321

Internal problem ID [4942]
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 : 321
Date solved : Tuesday, September 30, 2025 at 09:03:32 AM
CAS classification : [_linear]

\begin{align*} \left (x -2\right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 x y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

ode:=(x-2)*(x-3)*diff(y(x),x)+x^2-8*y(x)+3*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-\frac {1}{4} x^{4}+\frac {2}{3} x^{3}+c_1}{\left (x -3\right ) \left (x -2\right )^{2}} \]

✓ Mathematica. Time used: 0.079 (sec). Leaf size: 93

ode=(x-2)*(x-3)*D[y[x],x]+x^2-8*y[x]+3*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\frac {8-3 K[1]}{K[1]^2-5 K[1]+6}dK[1]\right ) \left (\int _1^x-\frac {\exp \left (-\int _1^{K[2]}\frac {8-3 K[1]}{K[1]^2-5 K[1]+6}dK[1]\right ) K[2]^2}{K[2]^2-5 K[2]+6}dK[2]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.266 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 + 3*x*y(x) + (x - 3)*(x - 2)*Derivative(y(x), x) - 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - \frac {x^{4}}{4} + \frac {2 x^{3}}{3}}{x^{3} - 7 x^{2} + 16 x - 12} \]