Internal problem ID [1791]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8.1, Singular points, Euler equations. Page 201
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {t^{2} y^{\prime \prime }-t y^{\prime }+2 y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve([t^2*diff(y(t),t$2)-t*diff(y(t),t)+2*y(t)=0,y(1) = 0, D(y)(1) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (\ln \left (t \right )\right ) t \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 10
DSolve[{t^2*y''[t]-t*y'[t]+2*y[t]==0,{y[1]==0,y'[1]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t \sin (\log (t)) \]