60.3.40 problem 1045

Internal problem ID [11036]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1045
Date solved : Wednesday, March 05, 2025 at 01:38:22 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

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

\[ y = {\mathrm e}^{x} \left (c_{1} \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (x -2\right )}{2}\right )+c_{2} \right ) \]

✓ Mathematica. Time used: 0.223 (sec). Leaf size: 34

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

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

✗ Sympy

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

False