67.3.21 problem Problem 22

Internal problem ID [14039]
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 22
Date solved : Tuesday, January 28, 2025 at 06:13:07 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+13 y^{\prime }&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1\\ y^{\prime \prime }\left (0\right )&=-6 \end{align*}

✓ Solution by Maple

Time used: 8.980 (sec). Leaf size: 16

dsolve([diff(y(t),t$3)+6*diff(y(t),t$2)+13*diff(y(t),t)=0,y(0) = 1, D(y)(0) = 1, (D@@2)(y)(0) = -6],y(t), singsol=all)
 

\[ y = 1+\frac {{\mathrm e}^{-3 t} \sin \left (2 t \right )}{2} \]

✓ Solution by Mathematica

Time used: 60.116 (sec). Leaf size: 73

DSolve[{D[ y[t],{t,3}]+6*D[y[t],{t,2}]+13*D[y[t],t]==0,{y[0]==1,Derivative[1][y][0] ==1,Derivative[2][y][0] ==-6}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^t\frac {1}{2} e^{-3 K[1]} (2 \cos (2 K[1])-3 \sin (2 K[1]))dK[1]-\int _1^0\frac {1}{2} e^{-3 K[1]} (2 \cos (2 K[1])-3 \sin (2 K[1]))dK[1]+1 \]