Internal problem ID [1792]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8.1, Singular points, Euler equations. Page 201
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1, y^{\prime }\relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 15
dsolve([t^2*diff(y(t),t$2)-3*t*diff(y(t),t)+4*y(t)=0,y(1) = 1, D(y)(1) = 0],y(t), singsol=all)
\[ y \relax (t ) = -t^{2} \left (2 \ln \relax (t )-1\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 15
DSolve[{t^2*y''[t]-3*t*y'[t]+4*y[t]==0,{y[1]==1,y'[1]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t^2 (1-2 \log (t)) \\ \end{align*}