73.13.20 problem 20.2 (b)

Internal problem ID [15398]
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 : Tuesday, January 28, 2025 at 07:54:26 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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