87.17.11 problem 11

Internal problem ID [23603]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 127
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:43:23 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 45

ode:=diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)-3*diff(diff(diff(diff(y(x),x),x),x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {x^{4}}{72}+\frac {c_3 \,x^{3}}{6}+\frac {c_4 \,x^{2}}{2}+\frac {{\mathrm e}^{-\sqrt {3}\, x} c_1}{9}+\frac {{\mathrm e}^{\sqrt {3}\, x} c_2}{9}+c_5 x +c_6 \]

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 62

ode=D[y[x],{x,6}]-3*D[y[x],{x,4}]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^4}{72}+c_6 x^3+c_5 x^2+c_4 x+\frac {1}{9} c_1 e^{\sqrt {3} x}+\frac {1}{9} c_2 e^{-\sqrt {3} x}+c_3 \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 6)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + C_{5} e^{- \sqrt {3} x} + C_{6} e^{\sqrt {3} x} - \frac {x^{4}}{72} \]