Internal problem ID [13301]
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 (e).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$4)-18*diff(y(x),x$2)+81*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-3 x} x +c_{3} {\mathrm e}^{3 x}+c_{4} {\mathrm e}^{3 x} x \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 35
DSolve[y''''[x]-18*y''[x]+81*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (c_3 e^{6 x}+x \left (c_4 e^{6 x}+c_2\right )+c_1\right ) \]