60.3.115 problem 1129

Internal problem ID [11111]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1129
Date solved : Wednesday, March 05, 2025 at 01:42:28 PM
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: 0.005 (sec). Leaf size: 29

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);
 

\[ y = 4 c_{2} \left (x^{3}-\frac {21}{2} x^{2}+\frac {75}{2} x -\frac {183}{4}\right ) {\mathrm e}^{3 x}+{\mathrm e}^{x} c_{1} \]

✓ Mathematica. Time used: 0.2 (sec). Leaf size: 90

ode=(-6 + 3*x)*y[x] - (-9 + 4*x)*D[y[x],x] + (-3 + x)*D[y[x],{x,2}] == 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