9.12 problem 15

Internal problem ID [1750]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

\[ \boxed {\left (1+2 t \right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y=0} \]

✓ Solution by Maple

Time used: 0.016 (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)
 

\[ y \left (t \right ) = c_{2} {\mathrm e}^{2 t}+c_{1} t +c_{1} \]

✓ Solution by Mathematica

Time used: 0.126 (sec). Leaf size: 23

DSolve[(2*t+1)*y''[t]-4*(t+1)*y'[t]+4*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

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