67.10.5 problem 15.2 (e)

Internal problem ID [16587]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.2 (e)
Date solved : Thursday, October 02, 2025 at 01:36:40 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 (1\right )&=0 \\ y^{\prime }\left (1\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.024 (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) = 0, D(y)(1) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 4 x^{3}-4 x^{2} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to 4 (x-1) 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): 0, Subs(Derivative(y(x), x), x, 1): 4} 
dsolve(ode,func=y(x),ics=ics)
 

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