Internal problem ID [13315]
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: 19.4 (c).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime }-4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$4)-3*diff(y(x),x$2)-4*y(x)=0,y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{-2 x}+c_{3} \sin \left (x \right )+c_{4} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 32
DSolve[y''''[x]-3*y''[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 e^{-2 x}+c_4 e^{2 x}+c_1 \cos (x)+c_2 \sin (x) \]