14.16.2 problem 16

Internal problem ID [2672]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.9, The method of Laplace transform. Excercises page 232
Problem number : 16
Date solved : Monday, January 27, 2025 at 06:06:13 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.843 (sec). Leaf size: 22

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

\[ y = \frac {\left ({\mathrm e}^{4 t}+24 \,{\mathrm e}^{\frac {3 t}{2}}+15\right ) {\mathrm e}^{-t}}{20} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 30

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

\[ y(t)\to \frac {1}{20} e^{-t} \left (24 e^{3 t/2}+e^{4 t}+15\right ) \]