Internal problem ID [12435]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number: 14.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 6
dsolve([diff(y(x),x$3)+diff(y(x),x)=0,y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 7
DSolve[{y'''[x]+y'[x]==0,{y[0]==1,y'[0]==0,y''[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos (x) \]