85.4.4 problem 1 (d)

Internal problem ID [22445]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. Section 1.3. A Exercises at page 21
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 08:39:37 PM
CAS classification : [[_3rd_order, _quadrature]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y \left (1\right )&=2 \\ y \left (2\right )&=9 \\ \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 14

ode:=diff(diff(diff(y(x),x),x),x) = 0; 
ic:=[y(0) = 1, y(1) = 2, y(2) = 9]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 3 x^{2}-2 x +1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 15

ode=D[y[x],{x,3}]==0; 
ic={y[0]==1,y[1]==2,y[2]==9}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 x^2-2 x+1 \end{align*}

✓ Sympy. Time used: 0.031 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 3)),0) 
ics = {y(0): 1, y(1): 2, y(2): 9} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 x^{2} - 2 x + 1 \]