Internal problem ID [13319]
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 (g).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {16 y^{\prime \prime \prime \prime }-y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(16*diff(y(x),x$4)-y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{\frac {x}{2}}+c_{2} {\mathrm e}^{-\frac {x}{2}}+c_{3} \sin \left (\frac {x}{2}\right )+c_{4} \cos \left (\frac {x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 41
DSolve[16*y''''[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/2} \left (c_1 e^x+c_3\right )+c_2 \cos \left (\frac {x}{2}\right )+c_4 \sin \left (\frac {x}{2}\right ) \]