59.1.183 problem 185

Internal problem ID [9355]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 185
Date solved : Sunday, March 30, 2025 at 02:33:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x \left (-x^{2}+7\right ) y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 47

ode:=x^2*diff(diff(y(x),x),x)-x*(-x^2+7)*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2} \left (\operatorname {Ei}_{1}\left (-\frac {x^{2}}{2}\right ) {\mathrm e}^{-\frac {x^{2}}{2}} c_2 \,x^{4}+c_1 \,x^{4} {\mathrm e}^{-\frac {x^{2}}{2}}+2 c_2 \,x^{2}+4 c_2 \right ) \]

✓ Mathematica. Time used: 0.213 (sec). Leaf size: 68

ode=x^2*D[y[x],{x,2}]-x*(7-x^2)*D[y[x],x]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{16} e^{\frac {1}{2} \left (-x^2-5\right )} \left (c_2 x^6 \operatorname {ExpIntegralEi}\left (\frac {x^2}{2}\right )+16 e^5 c_1 x^6-2 c_2 e^{\frac {x^2}{2}} \left (x^2+2\right ) x^2\right ) \]

✓ Sympy. Time used: 3.031 (sec). Leaf size: 889

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*(7 - x**2)*Derivative(y(x), x) + 12*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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