62.32.2 problem Ex 2

Internal problem ID [12908]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page 129
Problem number : Ex 2
Date solved : Monday, March 31, 2025 at 07:24:15 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

ode:=(x-3)*diff(diff(y(x),x),x)-(4*x-9)*diff(y(x),x)+(3*x-6)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_1 +c_2 \left (4 x^{3}-42 x^{2}+150 x -183\right ) {\mathrm e}^{2 x}\right ) \]

✓ Mathematica. Time used: 0.185 (sec). Leaf size: 90

ode=(x-3)*D[y[x],{x,2}]-(4*x-9)*D[y[x],x]+(3*x-6)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\left (\frac {3}{6-2 K[1]}-1\right )dK[1]-\frac {1}{2} \int _1^x\left (-4-\frac {3}{K[2]-3}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {3-2 K[1]}{2 (K[1]-3)}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 3)*Derivative(y(x), (x, 2)) + (3*x - 6)*y(x) - (4*x - 9)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False