71.9.13 problem 15

Internal problem ID [14492]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 06:42:26 AM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 12

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

\[ y = x \left (2-3 \ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 13

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

\[ y(x)\to x (2-3 \log (x)) \]