85.67.9 problem 9

Internal problem ID [22900]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 216
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:16:25 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{2 x} c_1}{4}-\frac {x^{2}}{4}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to -\frac {x^2}{4}+c_3 x+\frac {1}{4} c_1 e^{2 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.040 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{2 x} - \frac {x^{2}}{4} \]