13.7.7 problem 7

Internal problem ID [2370]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.2, linear equations with constant coefficients. Page 138
Problem number : 7
Date solved : Monday, January 27, 2025 at 05:50:28 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime }+5 y^{\prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.045 (sec). Leaf size: 34

dsolve([5*diff(y(t),t$2)+5*diff(y(t),t)-y(t)=0,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{\frac {3 t \sqrt {5}}{10}-\frac {t}{2}}-{\mathrm e}^{-\frac {t}{2}-\frac {3 t \sqrt {5}}{10}}\right ) \sqrt {5}}{3} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 42

DSolve[{5*D[y[t],{t,2}]+5*D[y[t],t]-y[t]==0,{y[0]==0,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} \sqrt {5} e^{-\frac {1}{10} \left (5+3 \sqrt {5}\right ) t} \left (e^{\frac {3 t}{\sqrt {5}}}-1\right ) \]