Internal problem ID [5990]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 83
Problem number: 5(b).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-k^{4} y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 5
dsolve([diff(y(x),x$4)-k^4*y(x)=0,y(0) = 0, D(y)(0) = 0, y(1) = 0, D(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 6
DSolve[{y''''[x]-k^4*y[x]==0,{y[0]==0,y[1]==0,y'[0]==0,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 0 \]