60.3.313 problem 1330

Internal problem ID [11309]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1330
Date solved : Thursday, March 13, 2025 at 08:47:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=-\frac {\left (A \,x^{2}+B x +C \right ) y^{\prime }}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )}-\frac {\left (\operatorname {DD} x +E \right ) y}{\left (x -a \right ) \left (x -b \right ) \left (x -c \right )} \end{align*}

✓ Maple. Time used: 1.033 (sec). Leaf size: 1147

ode:=diff(diff(y(x),x),x) = -(A*x^2+B*x+C)/(x-a)/(x-b)/(x-c)*diff(y(x),x)-(DD*x+E)/(x-a)/(x-b)/(x-c)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 12.144 (sec). Leaf size: 1166

ode=D[y[x],{x,2}] == -(((E + DD*x)*y[x])/((-a + x)*(-b + x)*(-c + x))) - ((C + B*x + A*x^2)*D[y[x],x])/((-a + x)*(-b + x)*(-c + x)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
A = symbols("A") 
B = symbols("B") 
C = symbols("C") 
DD = symbols("DD") 
E = symbols("E") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + (DD*x + E)*y(x)/((-a + x)*(-b + x)*(-c + x)) + (A*x**2 + B*x + C)*Derivative(y(x), x)/((-a + x)*(-b + x)*(-c + x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False