Internal problem ID [669]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= t^{2} \end {align*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 15
dsolve([t^2*diff(y(t),t$2)-4*t*diff(y(t),t)+6*y(t)=0,t^2],y(t), singsol=all)
\[ y \relax (t ) = c_{2} t^{3}+c_{1} t^{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[t^2*y''[t]-4*t*y'[t]+6*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t^2 (c_2 t+c_1) \\ \end{align*}