Internal problem ID [12768]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number: 9.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(diff(y(x),x$5)-diff(y(x),x$4)+diff(y(x),x$3)+35*diff(y(x),x$2)+16*diff(y(x),x)-52*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{4} {\mathrm e}^{4 x} \sin \left (3 x \right )+c_{5} {\mathrm e}^{4 x} \cos \left (3 x \right )+c_{1} {\mathrm e}^{3 x}+c_{3} x +c_{2} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 50
DSolve[y'''''[x]-y''''[x]+y'''[x]+35*y''[x]+16*y'[x]-52*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_4 x+c_5 e^{3 x}+c_2 e^{4 x} \cos (3 x)+c_1 e^{4 x} \sin (3 x)+c_3\right ) \]