Internal problem ID [15243]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.2 Homogeneous differential equations with
constant coefficients. Exercises page 121
Problem number: 453.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }=0} \] 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: 0.015 (sec). Leaf size: 10
dsolve([diff(y(x),x$3)+diff(y(x),x$2)=0,y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 1],y(x), singsol=all)
\[ y = {\mathrm e}^{-x}+x \]
✓ Solution by Mathematica
Time used: 0.096 (sec). Leaf size: 12
DSolve[{y'''[x]+y''[x]==0,{y[0]==1,y'[0]==0,y''[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x+e^{-x} \]