75.22.18 problem 723

Internal problem ID [17126]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 17. Boundary value problems. Exercises page 163
Problem number : 723
Date solved : Monday, March 31, 2025 at 03:42:37 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.043 (sec). Leaf size: 27

ode:=x^3*diff(diff(diff(diff(y(x),x),x),x),x)+6*x^2*diff(diff(diff(y(x),x),x),x)+6*x*diff(diff(y(x),x),x) = 0; 
ic:=y(1) = 0, D(y)(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -c_3 -c_4 +\left (-c_3 +c_4 \right ) \ln \left (x \right )+c_3 x +\frac {c_4}{x} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 34

ode=x^3*D[y[x],{x,4}]+6*x^2*D[y[x],{x,3}]+6*x*D[y[x],{x,2}]==0; 
ic={y[1]==0,Derivative[1][y][1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {(x-1) (c_1 (x-1)+2 c_2 x)}{2 x}-c_2 \log (x) \]

✓ Sympy. Time used: 0.117 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 4)) + 6*x**2*Derivative(y(x), (x, 3)) + 6*x*Derivative(y(x), (x, 2)),0) 
ics = {y(1): 0, Subs(Derivative(y(x), x), x, 1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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