29.11.27 problem 318

Internal problem ID [4918]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 318
Date solved : Tuesday, March 04, 2025 at 07:29:48 PM
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: 0.000 (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);
 

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

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 34

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]
 

\[ y(x)\to \frac {-3 x^4+8 x^3-12 c_1}{12 (x-3) (x-2)^2} \]

✓ Sympy. Time used: 0.430 (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)
 

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