Internal problem ID [13171]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.3 (d).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$4)=-2*diff(y(x),x$3),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} x +c_{3} x^{2}+c_{4} {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 28
DSolve[y''''[x]==-2*y'''[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{8} c_1 e^{-2 x}+x (c_4 x+c_3)+c_2 \]