28.3.3 problem 6.38

Internal problem ID [4516]
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 : 6.38
Date solved : Monday, January 27, 2025 at 09:22:36 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=2 t^{2}+1 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 2.766 (sec). Leaf size: 24

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

\[ y = -t^{2}+t +3 \,{\mathrm e}^{2 t}-2+5 \,{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 27

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

\[ y(t)\to -t^2+t+5 e^{-t}+3 e^{2 t}-2 \]