Internal problem ID [1785]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.8.1, Singular points, Euler equations. Page 201
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 15
dsolve(2*t^2*diff(y(t),t$2)+3*t*diff(y(t),t)-y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1}}{t}+c_{2} \sqrt {t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 20
DSolve[2*t^2*y''[t]+3*t*y'[t]-y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_2 t^{3/2}+c_1}{t} \\ \end{align*}