Internal problem ID [13308]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients.
Additional exercises page 369
Problem number: 19.2 (f).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+10 y^{\prime \prime }+18 y^{\prime }+9 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)+10*diff(y(x),x$2)+18*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
\[ y = {\mathrm e}^{-x} c_{1} +c_{2} {\mathrm e}^{-x} x +c_{3} \sin \left (3 x \right )+c_{4} \cos \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 38
DSolve[y''''[x]+2*y'''[x]+10*y''[x]+18*y'[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (c_4 x+c_1 e^x \cos (3 x)+c_2 e^x \sin (3 x)+c_3\right ) \]