Internal problem ID [11748]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients.
Exercises page 135
Problem number: 18.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$4)+8*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{4} x +c_{2} \right ) \cos \left (2 x \right )+\sin \left (2 x \right ) \left (c_{3} x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[y''''[x]+8*y''[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (c_2 x+c_1) \cos (2 x)+(c_4 x+c_3) \sin (2 x) \]