76.19.12 problem 12

Internal problem ID [17736]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 5. The Laplace transform. Section 5.4 (Solving differential equations with Laplace transform). Problems at page 327
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 11:02:00 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1\\ y^{\prime \prime \prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 10.518 (sec). Leaf size: 6

dsolve([diff(y(t),t$4)-y(t)=0,y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 1, (D@@3)(y)(0) = 0],y(t), singsol=all)
 

\[ y = \cosh \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 21

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

\[ y(t)\to \frac {1}{2} e^{-t} \left (e^{2 t}+1\right ) \]