72.19.2 problem 28

Internal problem ID [14960]
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 : 28
Date solved : Tuesday, January 28, 2025 at 07:25:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.682 (sec). Leaf size: 22

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

\[ y = \frac {13 \,{\mathrm e}^{-2 t}}{16}+\frac {{\mathrm e}^{2 t} \left (4 t +3\right )}{16} \]

✓ Solution by Mathematica

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

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

\[ y(t)\to \frac {1}{16} e^{-2 t} \left (e^{4 t} (4 t+3)+13\right ) \]