59.1.592 problem 608

Internal problem ID [9764]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 608
Date solved : Sunday, March 30, 2025 at 02:46:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (1+x \right ) y^{\prime \prime }-x \left (3+10 x \right ) y^{\prime }+30 x y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 65

ode:=x^2*(1+x)*diff(diff(y(x),x),x)-x*(3+10*x)*diff(y(x),x)+30*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 3 x^{4} \left (x -\frac {5}{2}\right ) c_2 \ln \left (x \right )+\frac {c_2 \,x^{6}}{4}+\frac {\left (16 c_1 -5 c_2 \right ) x^{5}}{8}+\frac {\left (-80 c_1 -299 c_2 \right ) x^{4}}{16}+5 c_2 \,x^{3}+\frac {5 c_2 \,x^{2}}{4}+\frac {c_2 x}{4}+\frac {c_2}{40} \]

✓ Mathematica. Time used: 0.485 (sec). Leaf size: 125

ode=x^2*(1+x)*D[y[x],{x,2}]-x*(3+10*x)*D[y[x],x]+30*x*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} (2 x-5) \exp \left (\int _1^x\frac {5-2 K[1]}{2 K[1]^2+2 K[1]}dK[1]-\frac {1}{2} \int _1^x\left (-\frac {7}{K[2]+1}-\frac {3}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\frac {4 \exp \left (-2 \int _1^{K[3]}\frac {5-2 K[1]}{2 K[1]^2+2 K[1]}dK[1]\right )}{(5-2 K[3])^2}dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(x + 1)*Derivative(y(x), (x, 2)) - x*(10*x + 3)*Derivative(y(x), x) + 30*x*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False