9.10 problem 13

Internal problem ID [1748]

Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 13.
ODE order: 2.
ODE degree: 1.

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

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 21

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

\[ y(t)\to c_2 t-c_1 (t-i)^2 \]