Internal problem ID [13300]
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: 19.1 (d).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-81 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$4)-81*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{3 x}+c_{3} \sin \left (3 x \right )+c_{4} \cos \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 36
DSolve[y''''[x]-81*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{3 x}+c_3 e^{-3 x}+c_2 \cos (3 x)+c_4 \sin (3 x) \]