59.1.477 problem 492

Internal problem ID [9649]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 492
Date solved : Sunday, March 30, 2025 at 02:39:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }+28 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

ode:=(x^2+1)*diff(diff(y(x),x),x)-10*x*diff(y(x),x)+28*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +\frac {35}{3} c_1 \,x^{4}-14 c_1 \,x^{2}+c_2 \,x^{7}+21 c_2 \,x^{5}-105 c_2 \,x^{3}+35 c_2 x \]

✓ Mathematica. Time used: 0.334 (sec). Leaf size: 93

ode=(1+x^2)*D[y[x],{x,2}]-10*x*D[y[x],x]+28*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*x*Derivative(y(x), x) + (x**2 + 1)*Derivative(y(x), (x, 2)) + 28*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False