Internal problem ID [11773]
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: 45.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+6 y^{\prime \prime }+2 y^{\prime }+5 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)+6*diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (2 c_{3} \cos \left (x \right ) \sin \left (x \right )+2 c_{4} \cos \left (x \right )^{2}-c_{4} \right ) {\mathrm e}^{-x}+c_{1} \sin \left (x \right )+c_{2} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 40
DSolve[y''''[x]+2*y'''[x]+6*y''[x]+2*y'[x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 \cos (x)+e^{-x} \left (c_2 \cos (2 x)+c_4 e^x \sin (x)+c_1 \sin (2 x)\right ) \]