Internal problem ID [5234]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 83
Problem number: 2.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 1, y^{\prime \prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 39
dsolve([diff(y(x),x$3)+y(x)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\sqrt {3}\, {\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+{\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )-1\right ) {\mathrm e}^{-x}}{3} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 53
DSolve[{y'''[x]+y[x]==0,{y[0]==0,y'[0]==1,y''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{-x} \left (e^{3 x/2} \left (\sqrt {3} \sin \left (\frac {\sqrt {3} x}{2}\right )+\cos \left (\frac {\sqrt {3} x}{2}\right )\right )-1\right ) \\ \end{align*}