74.15.60 problem 60

Internal problem ID [16499]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 60
Date solved : Tuesday, January 28, 2025 at 09:09:49 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 )&=0\\ y^{\prime }\left (-1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 12

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

\[ y = x \left (\ln \left (x \right )-i \pi \right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 15

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

\[ y(x)\to x (\log (x)-i \pi ) \]