75.22.15 problem 720

Internal problem ID [17194]
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 : Tuesday, January 28, 2025 at 09:56:52 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*}

✓ Solution by Maple

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

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

\[ y = 0 \]

✓ Solution by Mathematica

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

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

\[ y(x)\to 0 \]