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]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }-t y^{\prime }+2 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0, y^{\prime }\relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.009 (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)
\[ y \relax (t ) = t \sin \left (\ln \relax (t )\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (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]
\begin{align*} y(t)\to t \sin (\log (t)) \\ \end{align*}