67.10.6 problem 15.2 (f)

Internal problem ID [16588]
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 (f)
Date solved : Thursday, October 02, 2025 at 01:36:41 PM
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 (1\right )&=8 \\ y^{\prime }\left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 13

ode:=4*x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-y(x) = 0; 
ic:=[y(1) = 8, D(y)(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {5 x +3}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 16

ode=4*x^2*D[y[x],{x,2}]+4*x*D[y[x],x]-y[x]==0; 
ic={y[1]==8,Derivative[1][y][1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {5 x+3}{\sqrt {x}} \end{align*}

✓ Sympy. Time used: 0.105 (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(1): 8, Subs(Derivative(y(x), x), x, 1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 5 \sqrt {x} + \frac {3}{\sqrt {x}} \]