71.2.18 problem 10 (f)

Internal problem ID [14279]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 10 (f)
Date solved : Monday, March 31, 2025 at 12:15:14 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (2\right )&=-1 \end{align*}

✗ Maple

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = 0; 
ic:=y(0) = 2, D(y)(2) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0; 
ic={y[0]==2,Derivative[1][y][2]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

{}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) + 6*y(x),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 2): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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