72.19.3 problem 29

Internal problem ID [14961]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 6. Laplace transform. Section 6.3 page 600
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 07:25:38 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=2 \,{\mathrm e}^{t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 10.185 (sec). Leaf size: 21

dsolve([diff(y(t),t$2)-4*diff(y(t),t)+5*y(t)=2*exp(t),y(0) = 3, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = {\mathrm e}^{t}+\left (2 \cos \left (t \right )-4 \sin \left (t \right )\right ) {\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

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

\[ y(t)\to e^t \left (-4 e^t \sin (t)+2 e^t \cos (t)+1\right ) \]