Internal problem ID [1474]
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 10.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+12 y^{\prime \prime }+36 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$4)+12*diff(y(x),x$2)+36*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (\sqrt {6}\, x \right )+c_{2} \cos \left (\sqrt {6}\, x \right )+c_{3} \sin \left (\sqrt {6}\, x \right ) x +c_{4} \cos \left (\sqrt {6}\, x \right ) x \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 38
DSolve[y''''[x]+12*y''[x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (c_2 x+c_1) \cos \left (\sqrt {6} x\right )+(c_4 x+c_3) \sin \left (\sqrt {6} x\right ) \\ \end{align*}