67.3.14 problem Problem 15

Internal problem ID [14032]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number : Problem 15
Date solved : Tuesday, January 28, 2025 at 06:13:02 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-20 y^{\prime }+51 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-14 \end{align*}

✓ Solution by Maple

Time used: 9.128 (sec). Leaf size: 14

dsolve([diff(y(t),t$2)-20*diff(y(t),t)+51*y(t)=0,y(0) = 0, D(y)(0) = -14],y(t), singsol=all)
 

\[ y = -2 \,{\mathrm e}^{10 t} \sinh \left (7 t \right ) \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 18

DSolve[{D[y[t],{t,2}]-20*D[y[t],t]+51*y[t]==0,{y[0]==0,Derivative[1][y][0] ==-14}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{3 t}-e^{17 t} \]