Internal problem ID [670]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= t \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve([t^2*diff(y(t),t$2)+2*t*diff(y(t),t)-2*y(t)=0,t],y(t), singsol=all)
\[ y \relax (t ) = \frac {c_{1}}{t^{2}}+c_{2} t \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[t^2*y''[t]+2*t*y'[t]-2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {c_1}{t^2}+c_2 t \\ \end{align*}