67.8.39 problem 13.6 (e)

Internal problem ID [16534]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.6 (e)
Date solved : Thursday, October 02, 2025 at 01:36:09 PM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=10 \\ y^{\prime }\left (0\right )&=5 \\ y^{\prime \prime }\left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 13

ode:=diff(diff(diff(y(x),x),x),x) = diff(diff(y(x),x),x); 
ic:=[y(0) = 10, D(y)(0) = 5, (D@@2)(y)(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 8+3 x +2 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 15

ode=D[y[x],{x,3}]==D[y[x],{x,2}]; 
ic={y[0]==10,Derivative[1][y][0] ==5,Derivative[2][y][0] ==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 x+2 e^x+8 \end{align*}

✓ Sympy. Time used: 0.038 (sec). Leaf size: 12

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): 10, Subs(Derivative(y(x), x), x, 0): 5, Subs(Derivative(y(x), (x, 2)), x, 0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 x + 2 e^{x} + 8 \]