67.3.24 problem Problem 25

Internal problem ID [14042]
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 25
Date solved : Tuesday, January 28, 2025 at 06:13:09 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }+25 y^{\prime }&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=4\\ y^{\prime \prime }\left (0\right )&=-24 \end{align*}

✓ Solution by Maple

Time used: 8.954 (sec). Leaf size: 15

dsolve([diff(y(t),t$3)+6*diff(y(t),t$2)+25*diff(y(t),t)=0,y(0) = 1, D(y)(0) = 4, (D@@2)(y)(0) = -24],y(t), singsol=all)
 

\[ y = {\mathrm e}^{-3 t} \sin \left (4 t \right )+1 \]

✓ Solution by Mathematica

Time used: 60.116 (sec). Leaf size: 67

DSolve[{D[ y[t],{t,3}]+6*D[y[t],{t,2}]+25*D[y[t],t]==0,{y[0]==1,Derivative[1][y][0] ==4,Derivative[2][y][0] ==-24}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^te^{-3 K[1]} (4 \cos (4 K[1])-3 \sin (4 K[1]))dK[1]-\int _1^0e^{-3 K[1]} (4 \cos (4 K[1])-3 \sin (4 K[1]))dK[1]+1 \]