59.1.591 problem 607

Internal problem ID [9763]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 607
Date solved : Sunday, March 30, 2025 at 02:46:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} \left (1+x \right ) y^{\prime \prime }+4 x \left (3+8 x \right ) y^{\prime }-\left (5-49 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 40

ode:=4*x^2*(1+x)*diff(diff(y(x),x),x)+4*x*(3+8*x)*diff(y(x),x)-(5-49*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{3}+6 \ln \left (x \right ) c_2 \,x^{3}-18 c_2 \,x^{2}-9 c_2 x -2 c_2}{\left (1+x \right )^{4} x^{{5}/{2}}} \]

✓ Mathematica. Time used: 0.194 (sec). Leaf size: 104

ode=4*x^2*(1+x)*D[y[x],{x,2}]+4*x*(3+8*x)*D[y[x],x]-(5-49*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {K[1]+4}{2 K[1]^2+2 K[1]}dK[1]-\frac {1}{2} \int _1^x\frac {8 K[2]+3}{K[2]^2+K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {K[1]+4}{2 K[1]^2+2 K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*(x + 1)*Derivative(y(x), (x, 2)) + 4*x*(8*x + 3)*Derivative(y(x), x) - (5 - 49*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False