Internal problem ID [1718]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2, linear equations with constant coefficients. Page 138
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(t),t$2)-3*diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \relax (t ) = c_{1} {\mathrm e}^{\frac {\left (3+\sqrt {5}\right ) t}{2}}+c_{2} {\mathrm e}^{-\frac {\left (\sqrt {5}-3\right ) t}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 35
DSolve[y''[t]-3*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-\frac {1}{2} \left (\sqrt {5}-3\right ) t} \left (c_2 e^{\sqrt {5} t}+c_1\right ) \\ \end{align*}