54.3.382 problem 1399

Internal problem ID [12677]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1399
Date solved : Wednesday, October 01, 2025 at 02:19:30 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {\left (3 x +1\right ) y^{\prime }}{\left (x -1\right ) \left (x +1\right )}-\frac {36 \left (x +1\right )^{2} y}{\left (x -1\right )^{2} \left (3 x +5\right )^{2}} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 34

ode:=diff(diff(y(x),x),x) = 1/(x-1)*(3*x+1)/(1+x)*diff(y(x),x)-36*(1+x)^2/(x-1)^2/(3*x+5)^2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x -1\right )^{{3}/{2}} \sqrt {3 x +5}\, \left (3 c_2 \ln \left (x -1\right )+c_2 \ln \left (3 x +5\right )+c_1 \right ) \]

✓ Mathematica. Time used: 2.22 (sec). Leaf size: 137

ode=D[y[x],{x,2}] == (-36*(1 + x)^2*y[x])/((-1 + x)^2*(5 + 3*x)^2) + ((1 + 3*x)*D[y[x],x])/((-1 + x)*(1 + x)); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\frac {3 K[1] (K[1]+2)+7}{2 (K[1]-1) (K[1]+1) (3 K[1]+5)}dK[1]-\frac {1}{2} \int _1^x\frac {3 K[2]+1}{1-K[2]^2}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {3 K[1] (K[1]+2)+7}{2 (K[1]-1) (K[1]+1) (3 K[1]+5)}dK[1]\right )dK[3]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) - (3*x + 1)*Derivative(y(x), x)/((x - 1)*(x + 1)) + 36*(x + 1)**2*y(x)/((x - 1)**2*(3*x + 5)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False