28.3.16 problem 6.51

Internal problem ID [4529]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 6. The Laplace Transform and Its Applications. Problems at page 291
Problem number : 6.51
Date solved : Monday, January 27, 2025 at 09:22:48 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+4 y^{\prime }-4 y&=10 \,{\mathrm e}^{-t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=-2\\ y^{\prime \prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 3.373 (sec). Leaf size: 23

dsolve([diff(y(t),t$3)-diff(y(t),t$2)+4*diff(y(t),t)-4*y(t)=10*exp(-t),y(0) = 5, D(y)(0) = -2, (D@@2)(y)(0) = 0],y(t), singsol=all)
 

\[ y = 4 \cosh \left (t \right )+6 \sinh \left (t \right )+\cos \left (2 t \right )-4 \sin \left (2 t \right ) \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 28

DSolve[{D[y[t],{t,3}]-D[y[t],{t,2}]+4*D[y[t],t]-4*y[t]==10*Exp[-t],{y[0]==5,Derivative[1][y][0] == -2,Derivative[2][y][0] == 0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -e^{-t}+5 e^t-4 \sin (2 t)+\cos (2 t) \]