59.1.594 problem 610

Internal problem ID [9766]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 610
Date solved : Wednesday, March 05, 2025 at 07:58:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1+2 x \right ) y^{\prime \prime }+x \left (9+13 x \right ) y^{\prime }+\left (7+5 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 50

ode:=x^2*(2*x+1)*diff(diff(y(x),x),x)+x*(9+13*x)*diff(y(x),x)+(7+5*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {280 c_{2} \left (x +\frac {1}{2}\right )^{3} \left (x^{3}-\frac {9}{7} x^{2}+\frac {36}{35} x -\frac {4}{7}\right ) \sqrt {2 x +1}+143 c_{1} x^{2}+104 c_{1} x +20 c_{1}}{x^{7}} \]

✓ Mathematica. Time used: 0.54 (sec). Leaf size: 141

ode=x^2*(1+2*x)*D[y[x],{x,2}]+x*(9+13*x)*D[y[x],x]+(7+5*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{143} \left (143 x^2+104 x+20\right ) \exp \left (\int _1^x-\frac {15 K[1]+5}{4 K[1]^2+2 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {13 K[2]+9}{2 K[2]^2+K[2]}dK[2]\right ) \left (c_2 \int _1^x\frac {20449 \exp \left (-2 \int _1^{K[3]}-\frac {15 K[1]+5}{4 K[1]^2+2 K[1]}dK[1]\right )}{\left (143 K[3]^2+104 K[3]+20\right )^2}dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(2*x + 1)*Derivative(y(x), (x, 2)) + x*(13*x + 9)*Derivative(y(x), x) + (5*x + 7)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False