Internal problem ID [839]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-4 y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0, y^{\prime \prime }\relax (0) = 1, y^{\prime \prime \prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.051 (sec). Leaf size: 30
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)
\[ y \relax (t ) = \frac {3 \,{\mathrm e}^{t \sqrt {2}}}{8}+\frac {3 \,{\mathrm e}^{-t \sqrt {2}}}{8}+\frac {\cos \left (t \sqrt {2}\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 28
DSolve[{y''''[t]-4*y[t]==0,{y[0]==1,y'[0]==0,y''[0]==1,y'''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} \left (\cos \left (\sqrt {2} t\right )+3 \cosh \left (\sqrt {2} t\right )\right ) \\ \end{align*}