73.20.2 problem 29.6 (b)

Internal problem ID [15611]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 29. Convolution. Additional Exercises. page 523
Problem number : 29.6 (b)
Date solved : Tuesday, January 28, 2025 at 08:03:08 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 7.929 (sec). Leaf size: 14

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

\[ y = -\frac {\sin \left (2 t \right )}{8}+\frac {t}{4} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 17

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

\[ y(t)\to \frac {1}{4} (t-\sin (t) \cos (t)) \]