54.3.119 problem 1133

Internal problem ID [12414]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1133
Date solved : Wednesday, October 01, 2025 at 01:44:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x -1\right ) y^{\prime \prime }-\left (3 x -4\right ) y^{\prime }+\left (x -3\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.049 (sec). Leaf size: 31

ode:=(2*x-1)*diff(diff(y(x),x),x)-(3*x-4)*diff(y(x),x)+(x-3)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sqrt {2}\, \left (\left (\frac {c_1}{4}+c_2 \right ) \Gamma \left (-\frac {1}{4}, \frac {x}{2}-\frac {1}{4}\right )+\Gamma \left (\frac {3}{4}\right ) c_1 \right ) {\mathrm e}^{x -\frac {1}{4}}}{2} \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 93

ode=(-3 + x)*y[x] - (-4 + 3*x)*D[y[x],x] + (-1 + 2*x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x - 3)*y(x) + (2*x - 1)*Derivative(y(x), (x, 2)) - (3*x - 4)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False