59.1.536 problem 552

Internal problem ID [9708]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 552
Date solved : Sunday, March 30, 2025 at 02:44:51 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 28 x^{2} \left (1-3 x \right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y&=0 \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 23

ode:=28*x^2*(1-3*x)*diff(diff(y(x),x),x)-7*x*(5+9*x)*diff(y(x),x)+7*(2+9*x)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{2}+c_2 \,x^{{1}/{4}}}{-1+3 x} \]

✓ Mathematica. Time used: 0.278 (sec). Leaf size: 60

ode=28*x^2*(1-3*x)*D[y[x],{x,2}]-7*x*(5+9*x)*D[y[x],x]+7*(2+9*x)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\left (4 c_2 x^{7/4}+7 c_1\right ) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {6}{3 K[1]-1}-\frac {5}{4 K[1]}\right )dK[1]\right )}{7 x^{3/8}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(28*x**2*(1 - 3*x)*Derivative(y(x), (x, 2)) - 7*x*(9*x + 5)*Derivative(y(x), x) + (63*x + 14)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False