14.7.8 problem 8

Internal problem ID [2552]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.2. Linear equations with constant coefficients. Excercises page 140
Problem number : 8
Date solved : Monday, January 27, 2025 at 06:00:10 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=1\\ y^{\prime }\left (2\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.040 (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)
 

\[ y = \frac {\left (2+\sqrt {2}\right ) {\mathrm e}^{-\left (t -2\right ) \left (-3+2 \sqrt {2}\right )}}{4}-\frac {{\mathrm e}^{\left (t -2\right ) \left (3+2 \sqrt {2}\right )} \left (-2+\sqrt {2}\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 72

DSolve[{D[y[t],{t,2}]-6*D[y[t],t]+y[t]==0,{y[2]==1,Derivative[1][y][2] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{4} e^{-6-4 \sqrt {2}} \left (\left (2+\sqrt {2}\right ) e^{\left (3-2 \sqrt {2}\right ) t+8 \sqrt {2}}-\left (\left (\sqrt {2}-2\right ) e^{\left (3+2 \sqrt {2}\right ) t}\right )\right ) \]