Internal problem ID [672]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page
172
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= t \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 13
dsolve([t^2*diff(y(t),t$2)-t*(t+2)*diff(y(t),t)+(t+2)*y(t)=0,t],y(t), singsol=all)
\[ y \relax (t ) = c_{1} t +c_{2} t \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 16
DSolve[t^2*y''[t]-t*(t+2)*y'[t]+(t+2)*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t \left (c_2 e^t+c_1\right ) \\ \end{align*}