65.2.17 problem 10 (e)

Internal problem ID [15636]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 10 (e)
Date solved : Thursday, October 02, 2025 at 10:21:31 AM
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 )&=0 \\ y \left (2\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.040 (sec). Leaf size: 15

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

\[ y = \left (1+\left (x -2\right ) c_1 \right ) x^{2} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 23

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

\begin{align*} y(x)&\to \frac {1}{2} x^2 (x-c_1 x+2 c_1) \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 14

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): 0, y(2): 4} 
dsolve(ode,func=y(x),ics=ics)
 

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