7.8.15 problem 15

Internal problem ID [229]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.1 (Introduction. Second order linear equations). Problems at page 111
Problem number : 15
Date solved : Monday, January 27, 2025 at 02:42:46 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 )&=7\\ y^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 12

dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,y(1) = 7, D(y)(1) = 2],y(x), singsol=all)
 

\[ y = x \left (7-5 \ln \left (x \right )\right ) \]

✓ Solution by Mathematica

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

DSolve[{x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x] == 0,{y[1]==7,Derivative[1][y][1] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (7-5 \log (x)) \]