71.2.16 problem 10 (d)

Internal problem ID [14269]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises 1.3, page 27
Problem number : 10 (d)
Date solved : Wednesday, March 05, 2025 at 10:42:02 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^{\prime }\left (1\right )&=3\\ y^{\prime }\left (2\right )&=0 \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 15

ode:=x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x) = 0; 
ic:=D(y)(1) = 3, D(y)(2) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 13

ode=x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==0; 
ic={Derivative[1][y][1]==3,Derivative[1][y][2]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\left ((x-3) x^2\right ) \]

✓ Sympy. Time used: 0.163 (sec). Leaf size: 8

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 = {Subs(Derivative(y(x), x), x, 1): 3, Subs(Derivative(y(x), x), x, 2): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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