11.3.7 problem 14

Internal problem ID [1489]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 6.2, The Laplace Transform. Solution of Initial Value Problems. page 255
Problem number : 14
Date solved : Monday, January 27, 2025 at 04:57:54 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-4 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: 0.262 (sec). Leaf size: 21

dsolve([diff(y(t),t$4)-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)
 

\[ y = \frac {\cos \left (\sqrt {2}\, t \right )}{4}+\frac {3 \cosh \left (\sqrt {2}\, t \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 43

DSolve[{D[y[t],{t,4}]-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]
 

\[ y(t)\to \frac {1}{8} \left (3 e^{-\sqrt {2} t}+3 e^{\sqrt {2} t}+2 \cos \left (\sqrt {2} t\right )\right ) \]