60.3.320 problem 1337

Internal problem ID [11316]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1337
Date solved : Sunday, March 30, 2025 at 08:14:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

\[ y = \frac {\sqrt {x +b}\, c_1 +c_2}{\sqrt {\frac {x +a}{a -b}}} \]

✓ Mathematica. Time used: 0.109 (sec). Leaf size: 53

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

\[ y(x)\to \frac {c_1 \sqrt {a-b}+c_2 \sqrt {b+x}}{\sqrt {a-b} \sqrt {\frac {a+x}{a-b}}} \]

✗ Sympy

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

False