74.18.36 problem 42

Internal problem ID [16593]
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 : 42
Date solved : Tuesday, January 28, 2025 at 09:12:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 20

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

\[ y = \frac {17 \,{\mathrm e}^{2 t}}{16}+\frac {15 \,{\mathrm e}^{-2 t}}{16}-\frac {t}{4} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 16

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

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