59.1.805 problem 828

Internal problem ID [9977]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 828
Date solved : Sunday, March 30, 2025 at 02:50:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

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

\[ y = \frac {c_1 \,{\mathrm e}^{-3 x}+c_2 \left (9 x^{2}-6 x +2\right )}{x^{2}} \]

✓ Mathematica. Time used: 0.858 (sec). Leaf size: 52

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

\begin{align*} y(x)\to \frac {e^{-3 x} \left (\int _1^xe^{3 K[1]} c_1 K[1]^2dK[1]+c_2\right )}{x^2} \\ y(x)\to \frac {c_2 e^{-3 x}}{x^2} \\ \end{align*}

✓ Sympy. Time used: 1.548 (sec). Leaf size: 578

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

\[ \text {Solution too large to show} \]