13.13.3 problem 2

Internal problem ID [2433]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.8.1, Singular points, Euler equations. Page 201
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:52:42 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y = \frac {c_1 \,t^{{3}/{2}}+c_2}{t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 20

DSolve[2*t^2*D[y[t],{t,2}]+3*t*D[y[t],t]-y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {c_2 t^{3/2}+c_1}{t} \]