67.4.14 problem Problem 2(l)[n]

Internal problem ID [14058]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number : Problem 2(l)[n]
Date solved : Tuesday, January 28, 2025 at 06:13:20 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 y^{\prime \prime }+5 y^{\prime }-2 y&=7 \,{\mathrm e}^{-2 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.468 (sec). Leaf size: 18

dsolve([3*diff(y(t),t$2)+5*diff(y(t),t)-2*y(t)=7*exp(-2*t),y(0) = 3, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = -\left (-3 \,{\mathrm e}^{\frac {7 t}{3}}+t \right ) {\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 23

DSolve[{3*D[y[t],{t,2}]+5*D[y[t],t]-2*y[t]==7*Exp[-2*t],{y[0]==3,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

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