Internal problem ID [5367]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary
problems. Page 86
Problem number: 25.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$6)+9*diff(y(x),x$4)+24*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
\[ y = c_{1} \sin \left (x \right )+c_{2} \cos \left (x \right )+c_{3} \sin \left (2 x \right )+c_{4} \cos \left (2 x \right )+c_{5} \sin \left (2 x \right ) x +c_{6} \cos \left (2 x \right ) x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 40
DSolve[y''''''[x]+9*y''''[x]+24*y''[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (c_2 x+c_1) \cos (2 x)+c_6 \sin (x)+\cos (x) (2 (c_4 x+c_3) \sin (x)+c_5) \]