49.12.2 problem 1(c.2)

Internal problem ID [7675]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 3. Linear equations with variable coefficients. Page 108
Problem number : 1(c.2)
Date solved : Monday, January 27, 2025 at 03:09:39 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 13

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

\[ y = -\frac {1}{2 x}+\frac {x}{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 17

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

\[ y(x)\to \frac {x^2-1}{2 x} \]