Internal problem ID [1723]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2, linear equations with constant coefficients. Page 138
Problem number: 8.
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 }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 1, y^{\prime }\relax (2) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.1 (sec). Leaf size: 44
dsolve([diff(y(t),t$2)-6*diff(y(t),t)+y(t)=0,y(2) = 1, D(y)(2) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (2+\sqrt {2}\right ) {\mathrm e}^{-\left (t -2\right ) \left (-3+2 \sqrt {2}\right )}}{4}-\frac {{\mathrm e}^{\left (t -2\right ) \left (3+2 \sqrt {2}\right )} \left (\sqrt {2}-2\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 47
DSolve[{y''[t]-6*y'[t]+y[t]==0,{y[2]==1,y'[2]==1}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {1}{2} e^{3 t-6} \left (\sqrt {2} \sinh \left (2 \sqrt {2} (t-2)\right )-2 \cosh \left (2 \sqrt {2} (t-2)\right )\right ) \\ \end{align*}