73.13.20 problem 20.2 (b)

Internal problem ID [15319]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 20. Euler equations. Additional exercises page 382
Problem number : 20.2 (b)
Date solved : Thursday, March 13, 2025 at 05:54:31 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

With initial conditions

\begin{align*} y \left (4\right )&=0\\ y^{\prime }\left (4\right )&=2 \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 12

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

\[ y = \frac {4 x -16}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 15

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

\[ y(x)\to \frac {4 (x-4)}{\sqrt {x}} \]

✓ Sympy. Time used: 0.198 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = 4 \sqrt {x} - \frac {16}{\sqrt {x}} \]