54.3.239 problem 1255

Internal problem ID [12534]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1255
Date solved : Wednesday, October 01, 2025 at 01:57:15 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 42

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

\[ y = x^{a +1} c_2 \left (x -1\right )^{-a +1}+\left (a^{2}+a \left (2 x -1\right )+2 x^{2}-2 x \right ) c_1 \]

✓ Mathematica. Time used: 0.342 (sec). Leaf size: 129

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

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

✗ Sympy

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

ValueError : Expected Expr or iterable but got None