59.1.189 problem 191

Internal problem ID [9361]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 191
Date solved : Sunday, March 30, 2025 at 02:33:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=x^2*(x^2+1)*diff(diff(y(x),x),x)-x*(-x^2+5)*diff(y(x),x)-(25*x^2+7)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {4 c_2 \,x^{10}+5 c_2 \,x^{8}+c_1}{x \left (x^{2}+1\right )^{2}} \]

✓ Mathematica. Time used: 0.209 (sec). Leaf size: 110

ode=x^2*(1+x^2)*D[y[x],{x,2}]-x*(5-x^2)*D[y[x],x]-(7+25*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x-\frac {9 K[1]^2+7}{2 \left (K[1]^3+K[1]\right )}dK[1]-\frac {1}{2} \int _1^x\frac {K[2]^2-5}{K[2]^3+K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}-\frac {9 K[1]^2+7}{2 \left (K[1]^3+K[1]\right )}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(x**2 + 1)*Derivative(y(x), (x, 2)) - x*(5 - x**2)*Derivative(y(x), x) - (25*x**2 + 7)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None