65.2.15 problem 10 (c)

Internal problem ID [15634]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 10 (c)
Date solved : Thursday, October 02, 2025 at 10:21:28 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 (1\right )&=1 \\ y^{\prime }\left (2\right )&=-12 \\ \end{align*}

✓ Maple. Time used: 0.023 (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(1) = 1, D(y)(2) = -12]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -2 x^{3}+3 x^{2} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 14

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0; 
ic={y[1]==1,Derivative[1][y][2]==-12}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to (3-2 x) x^2 \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 10

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(1): 1, Subs(Derivative(y(x), x), x, 2): -12} 
dsolve(ode,func=y(x),ics=ics)
 

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