88.18.5 problem 5

Internal problem ID [24124]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 133
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:00:02 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }&=f \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

ode:=diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x) = f(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \int \int \left (\int f \left (x \right ) {\mathrm e}^{-x}d x +c_1 \right ) {\mathrm e}^{x}d x d x +c_2 x +c_3 \]

✓ Mathematica. Time used: 11.886 (sec). Leaf size: 53

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

\begin{align*} y(x)&\to \int _1^x\int _1^{K[3]}e^{K[2]} \left (c_1+\int _1^{K[2]}e^{-K[1]} f(K[1])dK[1]\right )dK[2]dK[3]+c_3 x+c_2 \end{align*}

✓ Sympy. Time used: 0.434 (sec). Leaf size: 37

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

\[ y{\left (x \right )} = C_{1} + x \left (C_{2} - \int f{\left (x \right )}\, dx\right ) + \left (C_{3} + \int f{\left (x \right )} e^{- x}\, dx\right ) e^{x} + \int x f{\left (x \right )}\, dx - \int f{\left (x \right )}\, dx \]