65.10.1 problem 17.1

Internal problem ID [13784]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 17, Reduction of order. Exercises page 162
Problem number : 17.1
Date solved : Tuesday, January 28, 2025 at 06:03:25 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using reduction of order method given that one solution is

\begin{align*} y&=t \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 12

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

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 17

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

\[ y(t)\to e t \left (c_2 e^t+c_1\right ) \]