85.61.8 problem 8

Internal problem ID [22862]
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 208
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:15:53 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime }&=x^{5}+1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=diff(diff(diff(y(x),x),x),x)-diff(y(x),x) = x^5+1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_1 -{\mathrm e}^{-x} c_2 -60 x^{2}-5 x^{4}-\frac {x^{6}}{6}-x +c_3 \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 43

ode=D[y[x],{x,3}]-D[y[x],{x,1}]==1+x^5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^6}{6}-5 x^4-60 x^2-x+c_1 e^x-c_2 e^{-x}+c_3 \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**5 - Derivative(y(x), x) + Derivative(y(x), (x, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- x} + C_{3} e^{x} - \frac {x^{6}}{6} - 5 x^{4} - 60 x^{2} - x \]