69.15.22 problem 453

Internal problem ID [18260]
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 ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 453
Date solved : Thursday, October 02, 2025 at 03:09:52 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }&=0 \end{align*}

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*}

✓ Maple. Time used: 0.055 (sec). Leaf size: 10

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x) = 0; 
ic:=[y(0) = 1, D(y)(0) = 0, (D@@2)(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = x +{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 12

ode=D[y[x],{x,3}]+D[y[x],{x,2}]==0; 
ic={y[0]==1,Derivative[1][y][0] ==0,Derivative[2][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x+e^{-x} \end{align*}

✓ Sympy. Time used: 0.044 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 0, Subs(Derivative(y(x), (x, 2)), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x + e^{- x} \]