13.9.12 problem 15

Internal problem ID [2398]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number : 15
Date solved : Monday, January 27, 2025 at 05:51:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 t +1\right ) y^{\prime \prime }-4 \left (1+t \right ) y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

dsolve((2*t+1)*diff(y(t),t$2)-4*(t+1)*diff(y(t),t)+4*y(t)=0,y(t), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{2 t}+c_1 t +c_1 \]

✓ Solution by Mathematica

Time used: 0.160 (sec). Leaf size: 23

DSolve[(2*t+1)*D[y[t],{t,2}]-4*(t+1)*D[y[t],t]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 e^{2 t+1}-c_2 (t+1) \]