74.18.37 problem 43

Internal problem ID [16594]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 43
Date solved : Tuesday, January 28, 2025 at 09:12:02 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 26

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

\[ y = \frac {\left (5 t +19\right ) {\mathrm e}^{-4 t} {\mathrm e}^{5 t}}{25}-\frac {19 \,{\mathrm e}^{-4 t}}{25} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 27

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

\[ y(t)\to \frac {1}{25} e^{-4 t} \left (e^{5 t} (5 t+19)-19\right ) \]