Internal problem ID [11728]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= t \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve([t^2*diff(y(t),t$2)-(t^2+2*t)*diff(y(t),t)+(t+2)*y(t)=0,t],y(t), singsol=all)
\[ y \left (t \right ) = c_{1} t +c_{2} t \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 16
DSolve[t^2*y''[t]-(t^2+2*t)*y'[t]+(t+2)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to t \left (c_2 e^t+c_1\right ) \]