Internal problem ID [13626]
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 (d).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-9 y^{\prime \prime }+31 y^{\prime }-39 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$3)-9*diff(y(x),x$2)+31*diff(y(x),x)-39*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{3 x} \left (c_{1} +c_{2} \sin \left (2 x \right )+c_{3} \cos \left (2 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 28
DSolve[y'''[x]-9*y''[x]+31*y'[x]-39*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x} (c_2 \cos (2 x)+c_1 \sin (2 x)+c_3) \]