Internal problem ID [13307]
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 (e).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+2 y^{\prime \prime }+4 y^{\prime }-8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)+diff(y(x),x$3)+2*diff(y(x),x$2)+4*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-2 x}+{\mathrm e}^{x} c_{2} +c_{3} \sin \left (2 x \right )+c_{4} \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 34
DSolve[y''''[x]+y'''[x]+2*y''[x]+4*y'[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 e^{-2 x}+c_4 e^x+c_1 \cos (2 x)+c_2 \sin (2 x) \]