75.22.15 problem 720

Internal problem ID [17115]
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 : 720
Date solved : Thursday, March 13, 2025 at 09:16:30 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 5

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-lambda^4*y(x) = 0; 
ic:=y(0) = 0, (D@@2)(y)(0) = 0, y(Pi) = 0, (D@@2)(y)(Pi) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 6

ode=D[y[x],{x,4}]-\[Lambda]^4*y[x]==0; 
ic={y[0]==0,Derivative[2][y][0] ==0,y[Pi]==0,Derivative[2][y][Pi]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 0 \]

✓ Sympy. Time used: 0.280 (sec). Leaf size: 3

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

\[ y{\left (x \right )} = 0 \]