Internal problem ID [14769]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x +y=0} \] With initial conditions \begin {align*} [y \left (-1\right ) = 0, y^{\prime }\left (-1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
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)
\[ y \left (x \right ) = \left (-i \pi +\ln \left (x \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 15
DSolve[{x^2*y''[x]-x*y'[x]+y[x]==0,{y[-1]==0,y'[-1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (\log (x)-i \pi ) \]