Internal problem ID [1472]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant
coefficient. Page 483
Problem number: section 9.2, problem 8.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x$4)+diff(y(x),x$2)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} x +c_{3} \sin \left (x \right )+c_{4} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 24
DSolve[y''''[x]+y''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_4 x-c_1 \cos (x)-c_2 \sin (x)+c_3 \]