60.2.30 problem Problem 41

Internal problem ID [15210]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 41
Date solved : Thursday, October 02, 2025 at 10:07:18 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (6\right )}-3 y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }&=x \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 48

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

\[ y = \left (c_3 \,x^{2}+\left (c_2 -6 c_3 \right ) x +c_1 -3 c_2 +12 c_3 \right ) {\mathrm e}^{x}-\frac {x^{4}}{24}-\frac {x^{3}}{2}+\frac {c_4 \,x^{2}}{2}+c_5 x +c_6 \]

✓ Mathematica. Time used: 0.105 (sec). Leaf size: 61

ode=D[y[x],{x,6}]-3*D[y[x],{x,5}]+3*D[y[x],{x,4}]-D[y[x],{x,3}]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x^4}{24}-\frac {x^3}{2}+c_6 x^2+c_3 e^x \left (x^2-6 x+12\right )+c_5 x+c_1 e^x+c_2 e^x (x-3)+c_4 \end{align*}

✓ Sympy. Time used: 0.081 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - Derivative(y(x), (x, 3)) + 3*Derivative(y(x), (x, 4)) - 3*Derivative(y(x), (x, 5)) + Derivative(y(x), (x, 6)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{6} e^{x} - \frac {x^{4}}{24} - \frac {x^{3}}{2} + x^{2} \left (C_{4} + C_{5} e^{x}\right ) + x \left (C_{2} + C_{3} e^{x}\right ) \]