Internal problem ID [5976]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 74
Problem number: 4(f).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$4)+5*diff(y(x),x$2)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = 2 c_{2} \cos \left (x \right )^{2}+\left (2 c_{1} \sin \left (x \right )+c_{4} \right ) \cos \left (x \right )+c_{3} \sin \left (x \right )-c_{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[y''''[x]+5*y''[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos (2 x)+c_4 \sin (x)+\cos (x) (2 c_2 \sin (x)+c_3) \]