58.8.7 problem 10

Internal problem ID [14676]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 113
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:50:07 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=3 \\ y^{\prime }\left (2\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 14

ode:=x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-4*y(x) = 0; 
ic:=[y(2) = 3, D(y)(2) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {x^{4}+32}{4 x^{2}} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 17

ode=x^2*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x]==0; 
ic={y[2]==3,Derivative[1][y][2]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^4+32}{4 x^2} \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - 4*y(x),0) 
ics = {y(2): 3, Subs(Derivative(y(x), x), x, 2): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x^{2}}{4} + \frac {8}{x^{2}} \]