Internal problem ID [1739]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2.2, Equal roots, reduction of order. Page 147
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(t),t$2)-6*diff(y(t),t)+9*y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{3 t} t \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 18
DSolve[y''[t]-6*y'[t]+9*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{3 t} (c_2 t+c_1) \\ \end{align*}