85.68.2 problem 2

Internal problem ID [22913]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 217
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:16:32 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {1}{2}\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 19

ode:=x^2*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-6*y(x) = 0; 
ic:=[y(1/2) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {c_1}{x^{3}}+\left (8-32 c_1 \right ) x^{2} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 22

ode=x^2*D[y[x],{x,2}]+2*x*D[y[x],{x,1}]-6*y[x]==0; 
ic={y[1/2]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {(8-32 c_1) x^5+c_1}{x^3} \end{align*}

✓ Sympy. Time used: 0.106 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 2*x*Derivative(y(x), x) - 6*y(x),0) 
ics = {y(1/2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} x^{2} + \frac {\frac {1}{4} - \frac {C_{2}}{32}}{x^{3}} \]