14.7.6 problem 6

Internal problem ID [2550]
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 : 6
Date solved : Monday, January 27, 2025 at 06:00:06 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+y^{\prime }-10 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=5\\ y^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 21

dsolve([2*diff(y(t),t$2)+diff(y(t),t)-10*y(t)=0,y(1) = 5, D(y)(1) = 2],y(t), singsol=all)
 

\[ y = \frac {29 \,{\mathrm e}^{-2+2 t}}{9}+\frac {16 \,{\mathrm e}^{\frac {5}{2}-\frac {5 t}{2}}}{9} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 30

DSolve[{2*D[y[t],{t,2}]+D[y[t],t]-10*y[t]==0,{y[1]==5,Derivative[1][y][1] ==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {16}{9} e^{-\frac {5}{2} (t-1)}+\frac {29}{9} e^{2 t-2} \]