Internal problem ID [13258]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 15. General solutions to Homogeneous linear differential equations. Additional
exercises page 294
Problem number: 15.7 (b).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)-10*diff(y(x),x$2)+9*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-3 x}+c_{3} {\mathrm e}^{-x}+c_{4} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 36
DSolve[y''''[x]-10*y''[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-3 x}+c_2 e^{-x}+c_3 e^x+c_4 e^{3 x} \]