Internal
problem
ID
[8360]
Book
:
DIFFERENTIAL
EQUATIONS
with
Boundary
Value
Problems.
DENNIS
G.
ZILL,
WARREN
S.
WRIGHT,
MICHAEL
R.
CULLEN.
Brooks/Cole.
Boston,
MA.
2013.
8th
edition.
Section
:
CHAPTER
7
THE
LAPLACE
TRANSFORM.
7.4.1
DERIVATIVES
OF
A
TRANSFORM.
Page
309
Problem
number
:
13
Date
solved
:
Monday, January 27, 2025 at 03:49:31 PM
CAS
classification
:
[[_2nd_order, _linear, _nonhomogeneous]]
Using Laplace method With initial conditions
✓ Solution by Maple
Time used: 0.872 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+16*y(t)=piecewise(0<=t and t<Pi,cos(4*t),t>= Pi,0),y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 60
DSolve[{D[y[t],{t,2}]+16*y[t]==Piecewise[{{Cos[4*t],0<=t<Pi},{0,t>=Pi}}],{y[0]==1,Derivative[1][y][0] ==1}},y[t],t,IncludeSingularSolutions -> True]