58.8.6 problem 9

Internal problem ID [14675]
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 : 9
Date solved : Thursday, October 02, 2025 at 09:50:06 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

With initial conditions

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 11

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

\begin{align*} y(x)&\to -((x-4) x) \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = x \left (4 - x\right ) \]