73.10.6 problem 15.2 (f)

Internal problem ID [15301]
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 : Tuesday, January 28, 2025 at 07:51:54 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 (1\right )&=8\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

dsolve([4*x^2*diff(y(x),x$2)+4*x*diff(y(x),x)-y(x)=0,y(1) = 8, D(y)(1) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 16

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

\[ y(x)\to \frac {5 x+3}{\sqrt {x}} \]