72.16.36 problem 38

Internal problem ID [14932]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number : 38
Date solved : Tuesday, January 28, 2025 at 07:21:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{-t}-4 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 23

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

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