59.1.589 problem 605

Internal problem ID [9761]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 605
Date solved : Wednesday, March 05, 2025 at 07:58:36 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} \left (2+3 x \right ) y^{\prime \prime }+x \left (4+21 x \right ) y^{\prime }-\left (1-9 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.043 (sec). Leaf size: 48

ode:=2*x^2*(3*x+2)*diff(diff(y(x),x),x)+x*(4+21*x)*diff(y(x),x)-(1-9*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sqrt {2+3 x}\, \sqrt {2}\, c_{2} +c_{1} x +3 \,\operatorname {arctanh}\left (\frac {\sqrt {2}\, \sqrt {2+3 x}}{2}\right ) c_{2} x}{\left (2+3 x \right )^{{3}/{2}} \sqrt {x}} \]

✓ Mathematica. Time used: 0.297 (sec). Leaf size: 102

ode=2*x^2*(2+3*x)*D[y[x],{x,2}]+x*(4+21*x)*D[y[x],x]-(1-9*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\left (\frac {1}{K[1]}-\frac {3}{12 K[1]+8}\right )dK[1]-\frac {1}{2} \int _1^x\left (\frac {15}{6 K[2]+4}+\frac {1}{K[2]}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {9 K[1]+8}{12 K[1]^2+8 K[1]}dK[1]\right )dK[3]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*(3*x + 2)*Derivative(y(x), (x, 2)) + x*(21*x + 4)*Derivative(y(x), x) - (1 - 9*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False