59.1.482 problem 498

Internal problem ID [9654]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 498
Date solved : Sunday, March 30, 2025 at 02:39:31 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x^{2}+4 x +5\right ) y^{\prime \prime }-20 \left (x +1\right ) y^{\prime }+60 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 65

ode:=(2*x^2+4*x+5)*diff(diff(y(x),x),x)-20*(1+x)*diff(y(x),x)+60*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{6}+c_1 \,x^{5}+\frac {5 \left (2 c_1 -15 c_2 \right ) x^{4}}{2}+5 \left (c_1 -20 c_2 \right ) x^{3}+\frac {5 \left (-4 c_1 -45 c_2 \right ) x^{2}}{4}+\frac {\left (-31 c_1 +120 c_2 \right ) x}{4}-\frac {7 c_1}{4}+\frac {155 c_2}{8} \]

✓ Mathematica. Time used: 0.569 (sec). Leaf size: 108

ode=(2*x^2+4*x+5)*D[y[x],{x,2}]-20*(x+1)*D[y[x],x]+60*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 1.076 (sec). Leaf size: 3

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-20*x - 20)*Derivative(y(x), x) + (2*x**2 + 4*x + 5)*Derivative(y(x), (x, 2)) + 60*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = O\left (1\right ) \]