64.8.7 problem 10

Internal problem ID [13395]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page 113
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 05:41:42 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

With initial conditions

\begin{align*} y \left (2\right )&=3\\ y^{\prime }\left (2\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 14

dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(2) = 3, D(y)(2) = -1],y(x), singsol=all)
 

\[ y = \frac {x^{4}+32}{4 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 17

DSolve[{x^2*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x]==0,{y[2]==3,Derivative[1][y][2]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^4+32}{4 x^2} \]