Internal problem ID [10946]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 5.5 Laplace transform. Homogeneous equations. Problems page 357
Problem number: Problem 13.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+y=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 0, y^{\prime \prime \prime }\left (0\right ) = \frac {\sqrt {2}}{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 55
dsolve([diff(y(t),t$4)+y(t)=0,y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 1/2*2^(1/2)],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (3 \,{\mathrm e}^{-\frac {\sqrt {2}\, t}{2}}+{\mathrm e}^{\frac {\sqrt {2}\, t}{2}}\right ) \cos \left (\frac {\sqrt {2}\, t}{2}\right )}{4}+\frac {\sin \left (\frac {\sqrt {2}\, t}{2}\right ) \left ({\mathrm e}^{-\frac {\sqrt {2}\, t}{2}}+{\mathrm e}^{\frac {\sqrt {2}\, t}{2}}\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 32
DSolve[{y''''[t]+y[t]==0,{y[0]==0,y'[0]==0,y''[0]==0,y'''[0]==1/Sqrt[2]}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \left (\frac {1}{4}+\frac {i}{4}\right ) \left (\sin \left (\sqrt [4]{-1} t\right )-\sinh \left (\sqrt [4]{-1} t\right )\right ) \\ \end{align*}